It is Kosovo to Serbs and Kosova to Albanians, just as it's Kosovo Polje to Serbs and Fushe Kosove to Albanians. Kosovo was originally settled by Serbs and many Albanian placenames are just corruptions of a Slavic root. But some are different. Serbs may call their town Urosevac, but it's Ferizaj to Albanians.
In Tito's benign era the road signs were all written in both languages. Now the use of either version is politically loaded. The BBC insists on Kosovo, as the province is legally part of Serbia. Robin Cook's preference for Kosova has been taken, probably mistakenly, as a sign of his support for the province's independence.