Changing their name to incorporate Manchester may help attract business sponsors other than that I don't see any benefit.

Agreed.
The Manchester moniker may help but, we're kidding ourselves if we think that a shinny club in Manchester is suddenly going to magic masses of new supporters, we're wrong.
I know that Salford isn't actually in Manchester but, their ground is only a spit away from Old Trafford and as another poster has mentioned, despite a new ground and riding high in the league, they aren't exactly turning fans away.
To really get a new "brand" out there, it will take a number of years of serious investment and there still wouldn't be any guarantee of success.

It's this or no club. That's the top and bottom of it.

There's no money in the game below SL level so clubs have to do what they have to do in order to survive.
If this helps the Lions get better sponsorship and improve their cash flow so they can improve as a club, then all the best to them

Which also isn't in Manchester but they do get lots of people watching Man. Utd. Is it because they have Manchester in their name or do people think Old Trafford is actually in Manchester?

Sale R.U. haven't changed their name and haven't played in Sale for a long time. Their crowds are alot better than Salford's, why is this?

Possibly because they draw from an enormous geographical and densely populated area ? I.e. the entire north west of England.
And they get between 6 and 8 thousand but often less.

It's official. Just waiting on sign off from the RFL

Is old traffird not in Manchester, last time i went it was and all the times before it was.

Old Trafford is in Trafford and Trafford is not and never has been in the city of Manchester.

Is it not in Greater Manchester?

Maybe they moved it from The Metropolitan Borough of Trafford to the City of Manchester just for you, good arn't they.

Yes, but Greater Manchester is a borough, not a town. I wish Swinton well, but it wont make a jot of difference, as people have said, Salford don't get supporters from the wider Manchester conurbation and it's 4 miles closer to Manchester.