He appears when SpongeBob is shown asleep because Mr. Krabs accidentally lulled him to sleep.
His name is a pun on the name "Barry."
SpongeBob once called him "SpongeBear Jr."
Beary was the first toy SpongeBob pulled out of the skill crane but he then pulled out a duplicate version of him when demonstrating the best crane technique to Squidward. The duplicate had then suddenly disappeared.