[Geoff Bacon]

I'm not sure that you can edit the name and have it immediately reflected in each song's metadata.

Suggest you amend one song so that it has the correct composer (this puts the correct name in the selectable items).
Then set a filter using the incorrect name as the search text.
Long press one of the songs until the check mark appears
Press the open square in the popup (bottom right) - this select all songs
Press Edit on top line
Select the correct Composer and OK
 
There may be other ways  but this should work

I believe there is a way to remove the incorrect composer from the selectable items but I can't remember how.

Geoff