Now New Orleans might lose the Saints to Los Angeles. If there's no place for them to play, then I suppose it does make some sense.
And it's the only place where this sort of name would be both appropriate and meaningful: The New Orleans Saints of Los Angeles. You've got a whole saints and angels thing too - which is kinda cool. Or would it be: The Los Angeles Saints of New Orleans? New Orleans Saints At Los Angeles?
However you phrase it - it is less idiotic than the Los Angeles Angeles of Anaheim, which, it was pointed out to me - and I hadn't really thought about before - translates to: the The Angels Angels of Anaheim. Der.