The official name of any sports Club is established in its constitution, which of course can be changed.
The majority of people who live in Swansea speak English so there is no huge desire to change it.
Welsh speakers call the City Abertawe and to be honest it wouldnt bother me if we changed our name to Abertawe.
As for road signs etc being in Welsh I suppose the tax payer is now paying the price for an attempted eradication of the Welsh language by the London government in the last century.
So, it's as I originally posted.
Despite talking about speaking Welsh, insisting on Welsh signs & singing about being Welsh you don't use the Welsh 'Abertawe' from choice

as you do!