Why are the episodes "Crocodile" and "Hang the DJ" named that way?

"Hang the DJ" is the chorus of the song "Panic" by the Smiths, which is played at the end of the episode. The gist of it is that the songs on the radio are meaningless to the singer and don't describe his life. My guess is that the various relationships they go through without each other were meaningless to them, hence they ended up with their 99.8% rating in the end.

Panic on the streets of London

Panic on the streets of Birmingham

I wonder to myself

could life ever be sane again?

the leeds side-streets that you slip down

i wonder to myself

hopes may rise on the grasmere

but honey pie, you're not safe here

so you run down

to the safety of the town

but there's panic on the streets of carlisle

dublin, dundee, humberside

i wonder to myself

Burn down the disco

hang the blessed dj

because the music that they constantly play

it says nothing to me about my life

hang the blessed dj

because the music they constantly play

on the leeds side-streets that you slip down

provincial towns you jog 'round

hang the dj, hang the dj, hang the dj hang the dj, hang the dj, hang the dj hang the dj, hang the dj, hang the dj hang the dj, hang the dj hang the dj, hang the dj hang the dj, hang the dj, hang the dj hang the dj, hang the dj hang the dj, hang the dj hang the dj, hang the dj, hang the dj hang the dj, hang the dj hang the dj, hang the dj hang the dj, hang the dj, hang the dj hang the dj

I think that "Crocodile" refers to the Crocodile tears :

The expression comes from an ancient anecdote that crocodiles weep for the victims they are eating. A collection of proverbs [...] suggests that the phrase "crocodile tears" was well known in antiquity: comparing the crocodile's behaviour to people who desire or cause the death of someone, but then publicly lament for them.
(Wikipedia)

I think this represents Mia who 'needs' to kill people to protect her secret but then cry and lament for what she did

My best guess is it's a homage to the pilot episode of Fargo, The Crocodile's Dilemma, which has some similar thematic elements:

...crashes a car at night on a wintry rural highway outside Bemidji, Minnesota, after hitting a deer

and a series of ever complicating mishaps, including

Lester... hits her with a hammer and kills her.

Googling "black mirror fargo" does pull up some other sources that note the similarity:

“Crocodile” contains numerous echoes of Fargo and A Simple Plan, similar morality tales set against similar desolate landscapes, and both stories of the totality of desperation and the futility of fate. Vox

Once you understand where “Crocodile” is heading, it’s already too late. The bleakness of its ever tightening spiral has already sucked you in, and you’re just left to reckon with it and its high body count. The knee-jerk reaction would be to say that this “Fargo in Iceland” vignette is dark for darkness’ sake — and that’s not necessarily an incorrect assessment — but buried beneath the bleak is a message about the unexpected ramifications of our increasingly connected society. Entertainment Weekly

"Hang the DJ" is definitely named after the song, as others have noted.

First let's talk about Hang the DJ:

Here you have to go through 1000 simulations to check compatibility but the twist is that the system will always try to separate you in one way or another and the right way to rebel against system is to prove your compatibility which Frank and Amy did 998 times out of 1000, making their compatibility level 99.8%.

Only time we hear the words Hang the DJ is in the end of episode where we hear The Smiths's song Panic, you can refer whole song's lyrics here, relevant part of lyrics goes as :

Burn down the disco
Hang the blessed DJ
Because the music that they constantly play
It says nothing to me about my life
Hang the blessed DJ
Because the music they constantly play

On the Leeds side-streets that you slip down
The provincial towns you jog 'round
Hang the DJ, hang the DJ, hang the DJ

Which shows the rebellion of the singer to the the DJ who is playing something which cannot be related to the singer. There are claims that this song was targeting a real DJ:

Legend has it that Morrissey and Johnny Marr wrote the lyric “Hang the DJ,” as a protest against a specific DJ named Steve Wright, whom they despised because of his insipid taste and adherence to a kind of corporate approach to music. So, the idea of singing “hang the DJ,” was about rejecting the music being played for you, to think for yourself, to rebel. - Source

Same applies for the episode where they have to rebel against the system to prove their compatibility. So Hang the DJ subtly hint on that real aim is not to make system do your match but to rebel against it like singer is rebelling against the DJ.

Now my take on Crocodile:

As Fabich's answer compared it to Crocodile Tear, which is not really wrong, her tear didn't appear that fake to me but looks more like psychotic tears. I don't see much of remorse as she was fine with killing as many people as she can to save herself. She is just being a psychotic selfish bitch who doesn't care about others if they come in her way, her tears have no meaning as she did nothing in her remorse like surrendering or anything like that, she played it like a pro. If there was no guinea pig she could have survived easily.

But there can be another angle too which is presented in Darth Locke's answer. I remember a famous animal fable from Panchatantra called The Monkey and The Crocodile.

It's a story of how crocodile was fine with sacrificing his best friend a monkey for his wife because she thinks monkey will be so tasty because he ate lots of red apples. It shows clear selfish motives of crocodile and this is not the only story/fable where crocodiles are represented in negative light. From Wikipedia page about Panchatantra:

The names connote the character observable in nature but also map a human personality that a reader can readily identify. For example, the deer characters are presented as a metaphor for charming, innocent, peaceful and tranquil personality who is a target for those who seek a prey to exploit, while crocodiles are presented as a symbolism for those with dangerous intent hiding beneath welcoming ambiance (waters of a lotus flower-laden pond)

So the episode title refers to the Mia's character who is selfish and ruthless while showing crocodile tears after doing a horrific act.

Crocodile Symbolism:

(Above: Sobek)

Crocodiles are featured across many religions and belief systems. Generally, crocodiles are often symbols of strength, fertility, and primal instincts and therefor can be symbols or metaphors for the concept of "self preservation". However in some religions, such as Christianity for instance, crocodiles can have an association with chaos and the devil with the idea being, one is destroyed from within.

(Leviathan: Serpant, Dragons, Etc)

In Bible crocodile is mentioned as one of the monsters of chaos. Because of this fact crocodile was later associated with the Devil in Christian symbolism. His natural enemy hydra kills him from inside like Jesus Christ destroyed Hell after having descended there for three days. Hydra represents Christ and crocodile stands for Hell. The hydra rolls itself into damp mud till its look is indistinguishable, and then makes its way into the mouth of the crocodile, which swallows it unawares, and instantly bursts asunder. During the Middle Ages stuffed crocodiles were chained on the walls of the churches. They represented chained Devil. http://symbols.ehibou.com/crocodile/

So how does this relate to the episode?

Crocodile is specifically about two woman, both MOTHERS, whose paths become intwined, with one women's abilty to do what she BELIEVES she needs to do, in order to survive (ie: not be held accountable, not be caught), but ironically, one accidentally becomes on the hunt for the other. It's a disturbing tale of misfortune by one women for people that are innocent.

It's a pyschological thriller & crime drama with one women almost uncautiously or complacently doing her job, with another relentless of being caught or trapped. Of course this is also personified through the episode's memory-sensory technology (Recaller), which furthers the pyschological aspect, because of the idea of accuracy of memory (which in itself can be subjective) vs if one can actively manipulate one's memory to produce major falshood?, which is distrubanly answered.

There are motifs and allusions pertianing to things one might characterisically associate with a crocodile throughout the episode, especially relating to the character Mia, but the crocodile is not the only animal featured, as there are allusions and reference to other animals, which then furthers the scope that this is about survival of fittest with people behaving like animals (Not unlike Thomas Harris' Hannibal Lector series).

Some Crocodile Motifs

1. Iceland as a primary location gives us a sense of "coldness" playing to the idea of being characteristically cold-hearted/cold-natured: detached, unfeeling, distant.

2. A building that Mia gives a conference in. The windows have a plant cell or "scale" motif, but it also could be compared to a crocodile eye, which is highly advanced being able to see several tragectories or targets, are retractable, and nocturnal, giving it a great tactical advantage.

3. Windows - Many characters are seen next to or looking out of windows. Windows are then used like "eyes" looking into other "eyes", shown through the memory sensory tech, as means for the insurance agent to follow the trail...

4. The memory sensory technology. The Recaller machine that conects to the chip, opens like a crocodile's mouth would.

5. Character Mia in partiuclar comes off with a crocodile-like dispostion, incuding a scene with an allusion to Crocodile Tears (fake sympothy), which is furthered by other scenes where the character only sheds tears as opposed to showing any other emotional response. There are also shots of the character's black "leather" shoes and it becomes clear that she is willing to go great distances to protect herself.

6. Insurance Company Costumer's Apartment with Animal Motif. Plants on shelves, large cat statue, zebra print throw-over, ect.