Definitely, when you've got your 'underware' (yes, I know, sic), everything fits better, feels better, is sorted out properly. Other things can go over it. It plays off of Webware, but implies both an underlying change and an underlying protocol. And the logo could be, well, a lot of fun, given the right mindset. Marketing it could be fun, too.
You could also extend the metaphor -- call it 'Knickers' or something.
"Hey, nice app, man, how did you write it?" "Um, with Underware." "What's that? Dude, yeah, I know, you work at home, but what did you write it in?" "Yeah, with Under- ... um. Man, just forget it ..."
When competing with Ruby on Rails we could have something like "Python in Panties", or "Webware in Woollies".
Python in Panties, especially, has a Monty Python twist:
"OHHHHH! I'm a lumberjack and I'm okay! I work all night and sleep all day ...
I cut down trees. I wear high heels, Suspendies, and a bra. I wish I'd been a girlie, Just like my dear Papa."
I rest my case.