"the Move"

So I'm in a band, and it's called 'the Move'. There also happens to be a 60's psychedelic rock band from the UK called 'the Move'. I did, however, join the band about a year after they started playing together, and had no say in the naming of the band. Obviously, I would have researched the name and found out immediately that it was not such a good idea.
Ironically (I think...) the three of us that are in the band now started playing together about two years ago and had a Myspace under the name "Bishop Delicious", which is actually still online. I like this name much more than our current moniker, and unless I'm missing something, it is totally original and has a lot more 'flavor'.
So... what are we to do? It wouldn't matter much at all if we were just a garage-band and never really got out, but now we're getting gigs every week, going out of town and playing at some semi-serious music festivals! We actually played at the Soundpony not too long ago, and they advertised us as from the UK.
This is not good. Not only can we be sued... but it's just awkward to have to answer those questions. "So, you're from the UK?", or "you know there's an issue with your name, there's already a band with a bunch of cd's called the Move."
I was also in the band "Megatron" (www.myspace.com/megatronband) and we recorded a cd under that name which should be out shortly. While there are a couple bands called "Megatron", none of them are very big, but of course there is a movie, a t.v. show, merchandise, etc...

So I guess I just don't know the 'actual rules' about this stuff, but I know we're breaking them now. Oh well?