How did Saruman know who Gimli was ?

[Inziladun]

Originally Posted by Rumil

More importantly, putting 2 and 2 together, Balin's occupation of Moria might have made him sit up and take notice. Saruman was the expert on Rings of Power, I bet he had figured out that there was still one of the seven unaccounted for, though I'm not sure if Gandalf let on that it was taken in Dol Guldur? If not, then Saruman would have loved to get his hands on it and Moria wasn't too far for his spies to travel, or to do a bit of Palantir-ing.

Saruman had to have been well aware Sauron had recovered or accounted for all the Seven.
Gandalf had gone into Dol Guldur in T.A. 2850, and had then found Thráin II there, raving about 'the last of the Seven'. The White Council had met the very next year to discuss what to do about the Necromancer (revealed to be Sauron by Gandalf), and Gandalf would surely have told all about his experiences in Dol Guldur, including the fate of Thráin's ring.