In Juliet's famous query, "Romeo! wherefore art thou Romeo?," she is essentially asking why Romeo's name must be Romeo. Her famous speech goes on to assert:
'Tis but thy name that is my enemy.
Thou art thyself, though not a Montague.
What's in a name? That which we call a rose
By any other name would smell as sweet. (II.ii.40-46)
She is essentially asserting here that names, as a part of language, are arbitrary. To be arbitrary means to be based on one's own relative perception or judgement, and those relative perceptions are also based on "personal whims [and even] prejudices" (Random House Dictionary). Since to be arbitrary is to be based on one's own relative ideas, to be arbitrary is also to be "unsupportable," or unlikely to endure and subject to change (Collins English Dictionary). Names are words, and words change per language, even though the words may be referring to the same object. In addition to words changing, there seems to be no concrete reasons for calling an object one word as opposed to another. Is there really any reason why we should call a rose a rose rather than say, a daisy? Juliet's answer to that question would be that there really is no specific reason--words and names are arbitrary. Hence, she is arguing in this passage that there really is no reason for Romeo to be named Montague as opposed to say, Smith, and that Romeo's surname Montague really has no direct bearing on who he is as a person.