You weren't looking up your T though - you were looking up him. It's fairly natural to take a look at someone's friend list to help confirm if it's the right person or not, and to see if they have anyone else that you both used to know.

It is certainly an uncomfortable coincidence though! You don't have to tell your T who it is, but you can see that you did look him up and that you looked at his friends list and saw that your T was on it. Whether you share his name with your T or not is sorta irrelevant.