I heard on many forums. After they "upgrade" the whole forum with a new skin or something. Than they say their forum v2.0. I'm not so sure what's that suppose to mean.
Anyway, my forum is also getting a total upgrade. Should i say "2.0"? Advertise Hotspot 2.0?
Well, i think that if that's what you want then go ahead. It sounds cool. I use versions to keep track of updates on my RPG forum, but that's about it.
They just want to sound "cool" (which also sounds lame), like software, eg. phpBB 3.0.7. The 3.0.7 is the version, but that's a legitimate way of naming it because of other things like MODs and themes, which need the correct version.
So to answer your question, no, you shouldn't. There isn't any need, and it's practically pointless.
David is right, I made a topic on my old forum about this whole "numbers in the name thing" and most of the comments thought the whole idea was stupid, and I agree. It means nothing it can also hurt your SERPs.
I have been on some real big forums that have done a massive total upgrade and they said they're site was version 2.0, but they didn't add it to the name of their site. Just stay with AH as the 2.0 at the end doesn't mean anything with just a new style etc.