The evidence from the books does not support this. King Robert has bastards with different surnames (Mya Stone, in the Vale; Edric Storms; in the Stormlands; Gendry Waters, in Kings Landing [unconfirmed, but come on]). The same can be said of Aegon IV’s many bastard children (Bittersteel and Bloodraven are Aegor and…

Bastard naming conventions are actually based on where the child is born, not on the parentage (hence why King Robert’s various bastards have names like Mya Stone, Edric Storm, etc...). Therefore, since the tower of joy is in Dorne, it should have been Jon Sands.