If you are talking about the built in RW form then I see your point. I’m not aware of any way to inject hidden fields which could be used to carry meta data to identify the form itself (not without hacking up the theme and code anyway).
Add ons like FormSnap and FormLoom from YabDab definitely can do this though - they are much more powerful and can be used to construct very sophisticated form solutions. You can find out more about FormSnap here:
My own contact form does something like this ( but is much less sophisticated than FormSnap or FormLoom ) - it adopts the simple approach of including the title of the form (which you can edit in settings) into the email you receive, so as long as you give your forms different titles you can tell them apart. You can see it here:-
There are other contact form stacks out there too. Doobox make a really fantastic one which I cannot recommend highly enough and also features a “form name” which addresses your concern: http://www.doobox.co.uk/stacks_store/demos/htmlcontact.html
Apologies if I missed any, there are plenty out there, I guess it just depends on how much of a form solution you really need.
Best of luck,