Why did they pick the title 'Tangled'?

In reference to the tangled connections between the characters.

Disney was originally going to call the movie Rapunzel Unbraided^[1]. However, after the failure of The Princess and the Frog^[2], Disney decided to take a hint from Pixar and make their titles more gender neutral:

Disney hopes the introduction of the slightly bad-boy character will help it tab the broadest possible audience for "Tangled", emulating the success of its corporate sibling, Pixar. Pixar's movies have been huge hits because they appear to girls, boys, and adults. Its most recent release, "Up", grossed more than $700 million worldwide.

"The Princess and the Frog" generated considerably less — $222 million in global ticket sales to date.

"Based upon the response from fans and critics, we believe it would have been higher if it wasn't prejudged by its title," Catmull said.
_(LAtimes)

Finally, they decided on "Tangled":

In rethinking "Rapunzel", Disney tested a number of titles, finally settling on "Tangled" because people responded to meanings beyond the obvious hair reference: a twisted version of the familiar story and the tangled relationship between the two lead characters.
_(ibid)

Nathan Greno:

The original intention was to make a film more closely related to something like Cinderella, where your main character is Cinderella, and there’s also a prince that’s in the movie that shows up once in a while. So we started developing: Okay, who is the male character in the show? We started playing around with scenes with our writer, Dan Fogelman, and doing this banter thing back and forth [between Rapunzel and Flynn]. And very early on, without realizing it, we were creating this duo. That’s what eventually lead to the title change. Just as you wouldn’t call Toy Story “Buzz Lightyear,” we really needed a title that represented what the film is, and that it’s a duo, and it stars Rapunzel and Flynn Ryder.

Ed Catmull, president of Pixar and Disney Animation Studios said:

We did not want to be put in a box. Some people might assume it's a fairy tale for girls when it's not. We make movies to be appreciated and loved by everybody.

It seems Disney is trying hard to capture the interest of more boys, which also explains their recent acquisition of the Marvel Comic universe.

What Floyd Norman, a retired Disney and Pixar animator told the LA Times:

The idea of changing the title of a classic like Rapunzel to Tangled is beyond stupid, I'm still hoping that Disney will eventually regain their sanity and return the title of their movie to what it should be. I'm convinced they'll gain nothing from this except the public seeing Disney as desperately trying to find an audience.

^{Google is always correct. And this too.}