It's a feminine form of Berengar/Berenger (Old German
, meaning "bear" + "spear"). Someone has submitted Berengar as a user-submitted name on this site - try searching here for it to see their entry.
This is the entry from the Withycombe Oxford:
Berengaria (f.): f. of Berenger (q.v.). The queen of Richard
I was named Berengière, which was Latinized as Berengaria. The name did not take root in England, but there have been children named Berengaria in Southampton in the present century after the well-known transatlantic liner of that name.
As another reader pointed out googling is nice, although it's better if you can get backup from something you know is more reliable - I usually don't trust a name site unless it's this one or I can find the same thing in a fairly reliable book.