When I was young, Ted was a common name for older adult men, and many were officially Edward. Bob (Robert) and Bill (William) were also popular names.
There are lots of Theodores, some will be Theo and some Teddy, and lots of Edwards, who may go by Teddy.
Teddy as a standalone name is #26 in England & Wales, so it seems very popular, and as a pp suggested will be a Neil/Gary/Ian of his generation. It will also be Ted as he gets older, and it just seems like an old man's name to me.
The first time I heard Teddy as a name it was on a footballer, and it was unusual enough to sound OK, and of course it helped that he was (and is) successful,talented and good-looking.
When I heard of Teddy as a name the second time, it was on a dog, and it seemed ridiculous.
I prefer the names Neil, Gary and Ian.