Klein provides the following etymology:
From Greek pandakion, from pandokos (= innkeeper, host; literally 'all-receiving'), which is compounded of pan (= every), which is of uncertain origin, and dokos, which stands in gradational relationship to dekesthai ( = to receive), from IE base *dek-, *dok- (= to take, receive, accept; acceptable, becoming, good).
More common Greek transliterations are pandocheion and pandokeion.
Kutscher points out that the word entered into Arabic as well as fundaq, and in an interesting turn of events, Crusaders from Europe borrowed the word from Arabic back into European languages as either an inn or a storehouse. So this led to the Romanian fundac, the Italian fondaco, the Portuguese alfandega, and the Spanish fonda.
While it would have been an interesting connection, it does not appear that the surname Fonda is related to the Spanish word for tavern.