Yeah football teams have nicknames but not all are well known. Commonly used ones are the Gunners for Arsenal, Spurs for Tottenham Hotspur, Wolves for Wolverhampton Wanderers... all clubs have nicknames but most of them are fairly obscure, like the Irons for West Ham Utd, the Toffeemen for Everton, and the Red Devils for Man Utd. I'm a Birmingham City fan, we're the Blues, we play in blue, it's a boring nickname but at least it's not cheesy. We also commonly get called Brum, the nickname of the city.

In terms of their official name, most English teams are either United, City or Town. Then there's Albion, Rovers and Wanderers, all used by multiple clubs in each case. I think those six cover the most commonly used names.