Teddy is diminutive form of name Ted.

Ted is an informal shortening of the name Edward.

Edward is an English name derived from the Anglo-Saxon Éadweard

Éadweard is a portmanteau of the words 'ead' meaning wealth or fortune and 'weard' meaning guardian or protector.

So Edward, or Teddy, mean protector of the wealth.

Bear is the word for bear, it means bear.

Now originally, a Teddy Bear, was not a toy but actually a replica bear (hence the 'bear' part of its name) and it was used by wealthy families to store their riches (hence 'teddy' or 'protector of the fortune') before safes had been invented, under the belief that burglars would mistake the toy for an actual sleeping bear and stay the fuck away.

Once safes had been invented storing your money in a sturdy metal box seemed far safer than the fake bear ruse, so people ditched the bears often just chucking them into the kids rooms for them to play with.

Unfortunately massive angry looking life sized bears tend to terrify young children, so slowly they were shrunk in size and anthropomorphised to look less horrifying thus resulting in the teddy bears we know today.