Note that more modern versions of D&D have leaned into the idea that an owlbear is literally a cross between an owl and a bear, but that's not how the creatures originally were presented in Greyhawk/AD&D. The owlbear comes directly from a set of cheap plastic toys that many people in the USA during the 70s (including Gary Gygax) found at bought at any drugstore: "Prehistoric Animals." The name owlbear, just like my description, was an attempt to describe the strange creature:

The creature came first, and people struggling to come up with a name called it an "owlbear," even though it contains the parts of neither owl nor bear.
This is the full set of toys you would get in the Prehistoric Animals bag (I had all these as a kid myself).

You will probably recognize at least a couple of other iconic D&D monsters there, too, whose designs/depictions have varied even less than the owlbear's.