Here's one for you old movie buffs: I was watching again, on DVD, the classic
film "TO HAVE AND HAVE NOT" a few days ago and noticed something. In the
picture, everyone else refers to Bogie's character, Harry Morgan, as "Harry."
But throughout the movie, Bacall's character calls him "Steve." No reason has
ever been given (that I know of). Does anyone have an explanation?

Probably for the same reason he called her "Slim". Just a nickname.

I've also heard that the director, Howard Hawks, and his wife used those as pet names for each other, so it was an inside joke for the characters in the movie to use them as well, but I don't know if that's really true or just a Hollywood myth.

She must have liked the name, because the first of their two children was
named Stephen. By the way, did you know Lauren Bacall was only 19 years
old when she made that movie? Of course, she looked older (her character
was supposed to be 23, I recall.)