Yes, in the quoted scene Juliet is asking why Romeo has to be a Montague with whom her family is feuding:

O Romeo, Romeo, wherefore art thou Romeo? Deny thy father and refuse thy name.

Or if thou wilt not, be but sworn my love And I’ll no longer be a Capulet.

‘Tis but thy name that is my enemy: 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 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, Take all myself.