Is it appropriate to use "reunion" for meeting only one person after a long time? If not, what's the alternative?
Solution 1:
There is nothing wrong with using the word reunion for as few as two people, although it is more commonly associated with groups. For instance, consider Paul Simon's song Mother and Child Reunion.
If you feel that the term makes it sound like a bigger event than it really was, try recasting it as "I reunited with an old friend" instead.
Solution 2:
It is perfectly correct to say you are having a reunion with an old friend. Indeed you could even say I was reunited with my old friend of 15 years ago.