Add setting to show/hide realm name.
Since currently it displays our chars like:

Realm Name
Character Name

I tend to quickly read the realm name for my chars instead their names so it gets confusing.

there is an option to only show current current realm (characters only on the current realm). how would you then show the realm if squashed to 1 line? Or just show the name only at that point and not worry about the realm?

I know about that option, but I meant only showing character name (not display realm name). I have unique names for my chars on various realms. My goal is to have the tooltip have as few things possible (for easier readability) while still displaying the information I want.
SavedInstances has a ton of configurable stuff on everything, have a look in the 2nd pic.
I know the end-goal would be to completely replace SavedInstances, but due to SI having tons of configurable things, I guess that goal will take a lot of time (maybe years) until all that kind of configuration (not exactly the same, anyway) is made available in LockedOut. I'm here to point out the things I miss from my use case/my point of view, whether this is feasible, doable or what kind of priority would it be asigned that's all yours to decide :)
PS: also that "show self first" option was really really useful.

example from Saved Instances

Saved Instances settings for displaying characters

done. realm name header is now configurable.