Every time this happens, it's one of two things:
You're sharing a computer and forgetting to log off. Maybe you're logging out of the site but not your OpenID provider, or you're still logged in to other sites. Log off of everything, or get used to using your browser's "private" mode on shared machines.
Your ISP sucks. Some internet providers set up caching proxies that are extremely poorly configured, and do stupid stuff like caching pages that we tell them not to cache. Assuming you've eliminated #1, contact your ISP or network administrator and
yell obscenities until they start cryingpolitely ask them to fix their network.
Update: Ah, I see the problem now - and don't worry, you're don't have access to anyone else's account. Way back in November of 2012, a moderator merged an unregistered account into yours. I don't know why - the reason is no doubt lost in the mists of time. Presumably he thought they were the same account. It later turned out that this was not the case, and the merge was reversed - but for some reason, the name stuck. Since it was an unregistered account, you don't have access to any personal information and the original owner of that account doesn't have any access to yours. There may be posts or comments that weren't automatically disassociated though - if you find something attached to your account that you didn't write, just flag it and request that it be disassociated.
Sorry for the confusion!