In the Wheel of Time series, we see that Lews Therin Telamon has 3 names, but the majority of the other characters and Forsaken in the book only have 2 names. Is it unique that he has 3? Is it of any significance?
It's significant but not unique.
From the companion volume The World of Robert Jordan's Wheel of Time (emphasis mine):
The people of [the Age of Legends] had long outgrown any interest in material wealth as a goal unto itself. Status and honour were all-important, and could only be gained through service to the community. All hoped to be allowed to serve according to their gifts and to be found worthy of that service. Several sources mention the fact that even names reflect a person’s status and honor. Everyone was born with two names and could earn the third one only through accomplishment, apparently possible in many fields.
There were several other people in the Age of Legends besides myself who are known to have had a third name, including eight of the thirteen Forsaken:
I'm at work, so I can't quote directly from the books until I get home, but the third name was granted to individuals who made great accomplishments. I seem to remember one book saying that one of the Forsaken was jealous that he never got a third name.
Is it unique? No. Looking in the WoT wiki shows that several of the forsaken have 3 names.
Ishamael: Elan Morin Tedronai
Rahvin: Ared Mosinel
Demandred: Barid Bel Medar
Sammael: Tel Janin Aellinsar
Aginor: Ishar Morrad Chuain
Balthamel: Eval Ramman
Asmodean: Joar Addam Nessosin
Be'lal: Duram Laddel Cham
Lanfear: Mierin Eronaile
Semirhage: Nemene Damendar Boann
Mesaana: Saine Tarasind
Graendal: Kamarile Maradim Nindar
Moghedien: Lilen Moiral
Is it significance? No. At least nothing suggests it. We even have at least one character with 4 names in their full name.