It was slightly different in that those nicknames / monikers tended to come about naturally e.g. Swinton Lions after the lions pub or the need to differentiate themselves from other sides like Rochdale FC / RFC (don't know which). They weren't created with the thought of flogging T-shirts or creating mascots. City Reds has that feel even if it was adopted in 1998.
how Fev ended up as Rovers but I like it.
IIRC The Rochdale Hornets club was an amalgamation of 2 or 3 clubs thus they wanted a new name and I think they wanted to differentiate themselves from another rugby club, Rochdale Rovers / Rangers. This happened in 1871.
Rochdale RUFC were formed in 1921.
Littleborough RUFC were formed as Old Rochdalians (from the grammar school) some time in the 20th century. You didn't have to have attended the grammar school to play for them but non-old boys were not allowed become full members and could not take part in any votes.
Rochdale FC were formed in 1907.