Put yourself in their shoes, if you transferred the money to someone by mistake, you'd want it back wouldn't you? Even if it was your fault.I think if the people look into it and claim they've sent it to the wrong person, I'd need to send the money back.
That is fine with me and I've just left it for now to see if anything comes up. I'd contact the bank before I'd think about taking the money though.
I don't mind leaving it for a bit longer but I'll contact them about closing the account as well as knowing where these funds are coming from, unless contacting them sooner might be better. I just don't really want to get into a whole process.
I say give it back, but that's cos I'd feel guilty about keeping it.