It resembles the German word Dom "cathedral" only in spelling but not in pronunciation, German Dom has a long closed o while the name Dom comes with a short o (middle or open).
It always reminds me of Dom Perignon, a trademark for champagne (real champagne from Champagne, France). The trademark is derived from the name of a benedictine monk who improved the production and quality of Champagne wine in an era when the region's wines were predominantly still red. Popular myths frequently, but erroneously, credit him with the invention of sparkling Champagne.In the case of Dom Perignon, Dom is not a given name but a title given to benedictine monks.
I would never name my child this. I really like it as a nickname for Dominic (it is way better than Nic), but I think it's too short to be an actual name.
People! It's actually short for Dominic. A sort of famous (but nontheless rather sexy) bearer is trans-Atlantic oarsman and polar explorer extraordinaire (as well as former Royal Marine) Dom Mee - could you want more of a man ladies?