It is a plural of berbí (type of tissue), although in Spanish it would be better formed as "berbíes". It could also be a mistake by Berberis ("barberry"), but I don't think so.
It is a surname of Canarian origin (Spanish). This surname is also found in the Valencian Community. Name of a dental clinic in Castellón.
berbís-belonging to the fabric or cloth of very thick fine hair also known by the name of "berbí cloth"-