Have you read Freakanomics?
Anyway, our two DDs have relatively unusual names (traditional ones, but neither are ever on the lists of possible names for anything) and we chose them by imagining seeing them written down.
Empty out all your openmindedness, and imagine you are a snotty university admissions person, or a job interviewer, or even an agent for artists.
Does the name make you think "self conciously eccentric, probably hippy, parents - will likely be a pain in the arse"? Or does it make you think "unusual name, but will stick in my mind, I wonder what they are like?"
Nicknames are fine - use whichever nicknames you like, the child can use it all their life - I know people who use relatively conventional names that have no relevance to their real name at all. But they need a formal name that doesn't speak too much for them.
It is also why names like Jayden, Kaycee, and so on are not a good idea. When people see the name on a form they form opinions about the person. Like it or not, that is what happens.
Jayden will be expected to be a bit rough, Bear to be a hippy, but (say) Edward will be expected to be...maybe slightly posh? Nothing drastic. Plus he will have loads of options nickanme wise. TBH he will probably get Bear/Teddy as a nickname anyway.
Imagine if "Bear" ends up overweight, or hairy. Or skinny and bald. Or a bit fighty. Or a wimp. Or big and gay. Or none of the above.
It suits him because he is a baby. Babies are cuddly and a bit grumpy. He won't always be a baby.
I can see what you were thinking, it is a very sweet name, but it needs to be a nickname and he needs a formal name that won't predjudice people against him.