Tavish comes from Tavis by way of the Scottish Clan MacTamhais, or anglicized phonetically MacTavish. The founder of the Clan MacTamhais was Taus(phonetically Tavis).
http://www.mactamhais.liquidweb.com/history.htm
I'm not sure if Taus (Tavis) actually translates to
Thomas or if that's just the
Christian name assigned to the Gaelic name, I know Tammas is the lowland
Scot form of
Thomas.