Llewyn Davis - connection to Llewelyn Davies family of Peter Pan fame ?

Maybe a silly thought, but I was watching 'Finding Neverland' and when I heard the name of the family whose children inspired the play 'Peter Pan', I was struck by the similarities between the family's name - Llewelyn Davies - and the name of the main character here.

Is this just happenstance? Or is it supposed to be a subtle nudge indicating that the Coen Brothers' Llewyn Davis is also a sort of 'Lost Boy', like the boys in the historical Llewelyn Davies family?

It's just a thought, but maybe someone else has an insight or two? Cause you have to admit that to a degree, our folksinger does live in a sort of Neverland, always trying to keep reality at bay and never really wanting to grow up aka. getting a regular job ...