I'd say yes.
This online dictionary shows two meanings, but one is a technical term and I have never heard "barber" used that way.
If you really want to study a vocabulary word, don't forget a good Etymology Dictionary:
barber Look up barber at Dictionary.com
early 14c., from Anglo-Fr. barbour (attested as a surname from 1221), from O.Fr. barbeor, barbieor (Mod.Fr. barbier, which has a more restricted sense than the English word), from V.L. *barbatorem, from L. barba "beard." Originally also regular practitioners of surgery and dentistry, they were restricted to haircutting and dentistry under Henry VIII. Barber-shop is from 1570s; in reference to close harmony male vocal quartets, it is attested from 1910.
weeelll yes and no. In the dictinary there are two, they're different and the same:
1.To trim or dress the hair or beard of.
2.Aperson whoose occupation is to trim or dress the hair or beard of customeres. (to trim or shave)