I feel pretty stupid about this, but despite having tried a number of times I can't work out how to change the names of members in a particular band.
Let's start by defining what you actually want to do: do you want to change the names of the people in the band, or do you want to change the lineup?
These are two very different procedures, since "band" is by definition a group of artists: members of the band are given by adding links - advanced relationships in the MusicBrainz language - between the members and the band.
So, if you want to change the lineup, you'll want to add a relationship between the new member and the band. If there was a person in the relationships that has never been in the band, you can remove the relationship between that person and the band. If the new member replaced someone, you'll probably want to edit the relationship between the former member and the band, and add end date - the day that person quit the band.
For example, The Rolling Stones has several member relationships in its page - you can see that the former members have both start and end dates defined so that we know they've quit the band. "Additional member" in this case means someone that's not part of the official lineup.
If you, on the other hand, want to actually change some band member's name, you'll want to edit that particular artist. If Rolling Stones' vocalist was actually Mitch Jagger, you'd probably want to go to his page and edit the artist to remove that pesky typo from his name ;)
Also, notice that we use the appropriate performance names when linking to band. For example, The Police has Sting as a member instead of Gordon Sumner, because that's the name he used when he was in The Police.
Check out my things to be fixed list in http://wiki.musicbrainz.org/ssundell
and holler if you fix something.