Is it a coincudence that all the guys of Big Time Rush happen to have the same names as the characters they're playing in the show???

No it's not. It was on purpose. Whatever the name of the actor was, the character was supposed to e named after him. Like; before Kendall was casted, there was a guy named Kurt who was supposed to play Kendall's role, but then they fond Kendall and this Kurt guy wasn't really that good... Anyway, when Kurt was on the show, the 'leader role' was named Kurt. I don't think the roles even had names to begin with. I think they had just created some personalities...

they did originally have names for their characters but Scott Fellows (the creator) thought they would be able to relate to their younger Fans if they had the same first name. that's what I heard

Scott Fellows the director,purposely made it that way so that way their younger Fans wouldn't get confused with real life and in the show.