Not sure if I'm forgetting any (it feels like I've seen more!), but these are all the gigs I can recall attending in Dorset over the years:
ZU2 at a pub in Bournemouth, July 2003. They used to have a website at http://www.zyworld.com/zu2/ but I believe they split up a few years ago. I'm gutted I only got to see them once - they were awesome but I missed their next gig and I don't think they ever played in my area again!
I did have tickets for a band called U2 2U in September 2003, but the gig was cancelled due to illness and never re-booked. I think it was mentioned that they were based way up in Scotland but I may be misremembering that.
Us4//U2 at a live music venue in Poole, February 2005. They carried on playing gigs there for years but I only went to see them once as I wasn't very impressed. Their website was at http://www.us4.org.uk/ but seems to be gone now - not sure if they're still around.
U2UK at a Bournemouth nightclub in December 2005 and a Wimborne theatre in September 2006. I then saw them again with a new singer at a Christchurch theatre in September 2009. They still seem to be active and have a website at http://www.u2ukshow.com/
U2Baby twice at a live music venue in Poole, April and December 2017 (plus I bumped into the singer and bassist while seeing the real U2 at Twickenham in between, haha). Their website is at http://www.theu2tributeuk.com/
A Sort Of U2 (a local group) at a pub in Branksome, June 2017. They have recently changed their singer from a man to a woman, so they probably sound quite different now! Their website is at http://asortofu2.com/ but it's hopelessly out of date - they mostly post updates on Facebook at http://www.facebook.com/asortofu2/
U2 2 (formerly known as Achtung Baby) at Bournemouth Air Festival, September 2018. Their website is at http://www.u2-2.com/