My son is 3 and still naps, once a day in the afternoon for 2 hours at least.
My daughter is 7, and she still occasionally naps when tired. She was still napping everyday afterschool even in 1st grade. She is now in 2nd grade.
My kids even though they nap, still sleep well at night and go to bed BY 8:30 nightly.
Your son, probably goes to bed too late. He is too overtired by then. Overtired kids, do NOT sleep well, nor solidly and they wake more. He does nap for a good length... which tells me he is tired and needs the nap. What time in the afternoon does he nap? Maybe its too late?
Also, at 2 years old, they normally do have sleep tweaks and aberrations. How long has he been doing that? Do you have a consistent daily regular sleep/nap routine EVERY day??? That is key. The SAME routine every day and night, pre-nap and pre-bed. This will cue the child.
Both my kids, had sleep tweaks at 2 years old. This is a common age in which this happens. It is usually a phase... and I KEPT to the same routine for my kids, through it.
Maybe your son does not need a nap. Right now. But, there will still be days when he will need one... so you have to gauge it and his "sleepy/tired" cues.
I can pretty much predict if my kids will nap or need a nap. For days I know they "cannot" nap, then we have a quiet time. They KNOW that.
Or, sometimes I tell them that MOMMY needs a nap, or is still sleeping.. .and I lay down. Then they usually follow suit. When my son is napping, my daughter KNOWS she has to be quiet and do quiet things... and if my son is awake and my daughter is napping or sleeping, my son KNOWS he has to be quiet. They both know.. .and do it.
But all kids are different, I know.
But, both my kids, no matter what, whether they had a nap or not, regardless what time they go to bed... they ALWAYS wake up at the same time in the morning. Its just them. Since they were babies.
All the best,
Susan