If you had written the adventure yourself this is something you may have decided when you wrote it, or it may be something you think about as the characters develop in playing, or a bit of both.
Personally, as there is no indication that Glassstaff has changed his appearance, there would be no reason that Sildar would not recognise him. Your role as DM is to play both NPCs reactions in accordance with your take on their personalities.
By the way, this is not something you can be wrong about.
Since the Lost Mines of Phandelver book does not specify this, it is your decision to make.
If Sildar recognizes Iarno it would most likely lead to more roleplay with diplomacy than fighting, as Sildar would probably want to ask questions as to why Iarno left and based off of Iarno's personality I think he would want to respond.
That aside, I would reccomend Sildar recognizing this person because
not having Sildar recognize Iarno will break immersion somewhat as it would seem a bit absurd that Sildar wouldn't recognize the man he was looking for when seeing him face-to-face.