I am going to assume that you're not referring to its capital city, which should be referred to by its official name "Palma" but to the whole island, yes?
For a bit of background:
During the dictatorship of fascist general Franco, in areas of non-Spanish(Castillian) culture -ie Balearic Islands, Catalonia, Basque Country...- names for many cities and towns were changed and new names imposed -mostly those that were in local languages or/and referred to local, hence "non-Spanish", events, historical figures, etc.. That was thankfully reverted after the dictatorship officially ended in 1978 and since most names have returned to what they originally had been.
In the case at hand, the fascists imposed "Palma de Mallorca" as the name of the capital city of the Balearic Islands when its name, since ancient times, had been simply "Palma". In time -as the dictatorship lasted four decades!-, many started to shorten its name to just "Mallorca" but that often caused confusion as the name of the island the city is in is also called "Mallorca". So what were you referring to? the city or the island as a whole?
As said, after the demise of Franco, the name of the city reverted to Palma but lots of people, especially overseas, still refer to it as "Palma de Mallorca" or its shortened variation "Mallorca" so confusion and misunderstandings remain. Btw, for info: most locals don't like their city being referred to as Palma de Mallorca, they (rightfully) insist the name of the city is "Palma" and the name of the island is "Mallorca".
Having clarified this, I hope these links can be of help to you: