The meaning and origin of the expression: A rose by any other name would smell as sweet

A rose by any other name would smell as sweet

What's the origin of the phrase 'A rose by any other name would smell as sweet'?

This is one of the best-known lines in Shakespeare's Romeo and Juliet, 1600:

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.

A story, much favoured by tour guides and as such highly suspect, is that in this line Shakespeare was also making a joke at the expense of the Rose Theatre. The Rose was a local rival to his Globe Theatre and is reputed to have had less than effective sanitary arrangements. The story goes that this was a coy joke about the smell. This certainly has the whiff of folk etymology about it, but it might just be true.