In this instance, Juliet is referring to the importance of a name in contrast to the essence of the object to which it refers. She is essentially saying that even if a rose was called something else it would retain its characteristics such as, for example, its sweet smell. She emphasizes that the name of something does not change its nature.
Juliet makes this remark in Act 2, scene 2. She has learnt that Romeo, the young man she is infatuated with, is a Montague. She is a Capulet and the two families have been involved in a squabble with each other for generations. This means that Romeo is her enemy and that she should not, therefore, have any association with him.
Juliet is quite distressed about the situation but does not allow it to affect her feelings for Romeo. Her sentiment is an expression of how deeply she feels for the young man. She has been overwhelmed by him and does not care whether he is a Montague or not. As far as she is concerned, it is not Romeo's name that makes him who he is. He could have had an entirely different name and she would have loved him all the same.
She has previously stated, though, that she would prefer it if he should abandon his name and deny his heritage. If he cannot do so, she will be happy if he should declare his love for her. She will then, in turn, forsake her own name:
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.
She does not believe that being a Montague means that she should dismiss him. Montague, is after all, only a meaningless name and does not constitute any integral part of a body. Romeo shares this sentiment. He expresses his own sentiments after hearing what Juliet has said about the matter:
I take thee at thy word:
Call me but love, and I'll be new baptized;
Henceforth I never will be Romeo.
The two impetuous lovers then embark on a very dangerous affair fraught with risk and complication. Their overwhelming passion and naive belief that their love will persevere eventually ends in tragedy.
As she stands on her balcony in Act 2, Scene 2, Juliet is trying to reconcile in her mind the fact that the man that she has just experienced love at first sight with is none other than a Montague, and, specifically, the son of her family's great enemy.
In her musings, she mentions that it is Romeo's name (Montague) and not Romeo himself who is the enemy. It is then that she utters the next lines:
What’s in a name? That which we call a rose By any other word would smell as sweet. ...
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So Romeo would, were he not Romeo called, Retain that dear perfection which he owes Without that title. (Act 2, Scene 2, lines 43-47).
Juliet is making an analogy here. Essentially, she is saying that names are meaningless. A rose would smell sweet whether we called the object a "rose" or a "thumple" or a "gobbeldythwacker" (I am making up these names here -- Juliet didn't come up with these!). Likewise, Romeo would be just as perfect even if his name were not Romeo Montague.
In the lines that follow, Juliet states that she wishes that Romeo would trade in his name, and that he could have her instead. It is at this point that Romeo reveals he has heard this, and that he has been hiding in the bushes nearby all along.
The quotation is actually a very profound one. It suggests that a name is simply a label to distinguish something from another. It does not create worth nor does it create true meaning. What is important is the worth of the individual or thing. A rose, if called something entirely different, would still smell as sweetly as it does with the name "rose." Juliet likens this to Romeo - Romeo is still the man she loves had he a different name. What is his name but, simply, a label. It does not define him as a man.
This, of course, is relevant because the Capulets (her family) and the Montegues (Romeo's family) loathe each other. To be in love would be forbidden simply because of their names. What Juliet exposes is the ridiculousness of the feud between the two families over, simply, who they are. What the feud is about is, therefore, unknown and irrelevant.
This quote suggests Shakespeare's belief that a name means little - it is the worth of the individual that counts.
The quotation 'what's in a name...' from the play Romeo and Juliet by William Shakespeare as spoken by Juliet in the so-called 'balcony scene' foreshadows the words of Mercutio ' a plague on both your houses.' In old Europe, the idea of dynasty was very important and that could be referred to by mention of family, 'house' , arms or heraldry - all were similar and showed lineage of status that went back generations. So the names of Montague and Capulet went very far back and engendered either hatred or loyalty depending on one's allegiance or dependency. So Juliet's childlike comment shows either innocence or naievte (she loved Romeo whatever he was callled) - but for what was in a name the locals would fight to death- with terrible consequences.
What she means here is that she does not care what Romeo's name is and she wishes he would just take the name off and be someone else so that their families would not be enemies.
She says this when she is up on her balcony but before she knows Romeo is there. He's listening, but she does not know it.
So what she is saying here is that it does not matter what Romeo's name is. If you call a rose something else, it still smells the same. And if Romeo had a different name he would still be the man she loves.