Well, they aren't from the same language but they are from related languages. Celt languages today can be divided into Brythonic/British (P-Celtic if you want to sound very science-y ;o) - Welsh, Cornish, Breton and Goidelic/Gallic (Q-Celtic) - Irish Gaelic, Scottish Gaelic and Manx (Isle of Man).
Now where the idea that Brian meant 'hill' came from is beyond me. The official stance of etymology is that it's unknown but *probably* from the Old Celtic for 'high, noble'. I suppose they're assuming a connection to beann/beinn (top, peak) but that's still nothing more than assumption...though if all one wants is a straightforward 'meaning', full-on accurate or not, it'll do nicely.