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Ulaid may be the Irish word for Ulster (Northern Ireland).

Yes, a tribal name, or name of a population group in my preferred terminology. Also, as was customary in medieval Ireland, the name transfered to the territory inhabited by the Ulaid, "...between Dundrum Bay and Belfast Lough" (F.J.Byrne, "Irish Kings and High Kings"). As the Ulaid territory was once much larger the name sometimes was, and now is, used to identify the province of Ulster.
But it is not a surname, though one surname, Mac Con Ulaidh, incorporates the name. It means "son of Cu Ulaidh" a male given name meaning "hound of Ulster". This name, according to Edward MacLysaght, has become MacNally in its English language version.
There is also the surname Mac an Ultaigh (MacNulty), "son of the Ulidian", or man of Ulster in its narrower meaning.