I have this question, too. Hoping this is a bug that will get fixed in the next round of updates. My Messages app itself still shows their first and last name as I like it, so why is it changing between screens? It ought to be synced where if ‘Short Name’ or ‘Prefer Nicknames’ is toggled on, then and only then should their short/nicknames appear on one’s lock screen.
Also, don’t want contact photos showing next to the name on my Messages lock screen when I have ‘Show Contact Photos’ toggled off. Most of my contacts don’t have photos, so there is no need to include a gray shadow figure next to each of those contacts. Again, this should be synced with the toggle option, like the naming convention. @Apple please fix these bugs!