Sporting fans really don't like it since it isn't part of their name.
Bilbao (or Bilboko) features in both the Spanish and Basque official names for Athletic and in their badge, so not really the same.
I doubt many people around the world refer to Arsenal as Arsenal London by just randomly adding a word to their name that isn't in it.
From wiki:
The designation "Sporting Lisbon", a common way some foreign media and non-Portuguese speaking people use to refer to Sporting CP outside Portugal,[1] has been a source of contention and controversy for some sportinguistas[135][2] because it does not conform with the official name of the sports club and its brand value.[136] Regarding this issue, club supporters and officials have promoted awareness campaigns to raise people's awareness nationwide and internationally, and the club changed its official crest in 2001[137] with a focus on the name of the club and its words "Sporting" and "Portugal" in mind.[4][138][139][5]