A Namely Personality

Claire Colburn: Never met a Mitch I didn't like. Fun, full of life. Like... everyone wants to be a part of Mitch's club. 

-- Elizabethtown

Are names something to spark the personality, so that those with the same name also have some of the same characteristics? 

JULIET:

'Tis but thy name that is my enemy.(40) 
Thou art thyself, though not a Montague. 
What's Montague? it is nor hand, nor foot, 
Nor arm, nor face, nor any other part 
Belonging to a man. O, be some other name! 
What's in a name? That which we call a rose(45) 
By any other name would smell as sweet. 
So Romeo would, were he not Romeo call'd, 
Retain that dear perfection which he owes 
Without that title. Romeo, doff thy name; 
And for that name, which is no part of thee,(50) 
Take all myself. 

-Shakespeare

But if the name brings personality to the character?, how then, can one just vanquish a name? Romeo doesn't lose his name throughout the play, and there has to be some significance in that... And like Romeo, Owen reclaims his in Act 2... so if it is just a name, why is everyone so hesitant to toss theirs to the wayside, but toss another's up to the chopping block?