While we might think the word "wherefore" means "where," it actually means "why." In this exclamation, therefore, the anguished Juliet is asking Romeo why he is Romeo, meaning, why is he a Montague?
Juliet has fallen in love with Romeo at this point, which is the balcony scene in act II. She understands, however, that his being of the house of Montague, with which her family is feuding, makes their relationship forbidden. She goes on, in her speech to Romeo, to express how senseless it is that she should be expected to hate someone she loves merely because of his name. She makes a distinction between a label, such as "Montague," and the reality of what the person is beneath the label, stating:
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.
She will then go on to make the famous statement about a rose by any other name smelling as sweet. She shows she is a person capable of thinking for herself.
The names "Romeo" and "Montague" stand for any names which obscure what is good under a negative label.