Where there any other Master who didn't know their Servant's identity from the start?
If you just want them to be unknown at the beginning, then in Fate/Zero Uryuu did not know who his Caster ("Bluebeard") was.  Much like Shirou, Uryuu was not even aware that he was summoning a servant until Bluebeard showed up.  Unlike Shirou, he wasn't even aware that magic really existed.  He was just doing the ritual in the occult book he had for the fun of it.

While Bluebeard tells Uryuu his nickname of "Bluebeard" right away, it is unclear if Uryuu knows who this refers to.  I'm not sure if it is ever mentioned if Uryuu ever learned the true identity of his Servant.  They had a weird relationship, with Uryuu largely seeing Bluebeard as a kindred spirit and teacher, and they never really cared about the formalities of the war or what they were "supposed" to be doing in it.  They were definitely on good enough terms for Bluebeard to share the information, but they simply may not have cared about it.