Where did "Nemo Nobody" get his name?

In the movie Mr.Nobody the character played by Jared Leto is called "Nemo Nobody" as in the First Name Last Name syntax. This we see when Nemo kisses Elise in the car just before the explosion, smiles and days "Mrs. Nobody"

My Question: How did he(Jared Leto's character) come to own this name?

1. Did he give it to himself?
2. My guess is: in the movie at 18:49 during kid Nemo's monologue of "Do I exist" we see his mother reciting this poem "Eenie meenie minie mo". Does the kid Nemo take this verse to be "My Nemo" instead of "minie mo" and thus assume that must be his name? And may be later on, on learning Nemo means Nobody, takes his name as this?

I could not find any reference to this verse in the context of Nemo's naming anywhere. Any help would be great.