What is the allusion in the phrase 'by any other name'?

The allusion is to Shakespeare's play, Romeo and Juliet. Romeo and Juliet had a forbidden romance, because their respective families were feuding. Juliet is thinking about the difficulties caused by their names, being from the quarreling families, and says:

JULIET:

'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. Her point is that a name is less significant than the substance it signifies, and that phrase has often been quoted, in many contexts.