Yes they discuss her name. But if you recall Jessie liked her name and enjoyed the secret thrill of its salacious implication exactly because she is quite a square in real life. However Elijah one day reads the Bible and gives her the more correct interpretation of Jezebel's behaviour as that of a woman protecting her interests and not at all a harlot. This greatly upsets Jessie because it robs her of that secret thrill. She then never uses the full name again. Elijah often regrets this.

Despite its intricacies I found this particular part of their marital back story to be totally unconvincing and ineffective. Sorry Isaac.