Are Sharpies real paint markers? I work with paint markers often and they're really suitable. One condition though is that you can't (or very difficult) draw over wet oils. An option would be that you create, in acryl or gesso, some sort of rock at the side where you can write their names on after you finished the painting.
Or even better, write it in the sand!!
A possible example would be 'Island paradies' S27E9 where you have quite some rock. Another would be 'Ocean sunset' S10E10 where you have quite some sand.
If you are brave enough Heather .... you still might try thinning your paint enough for the scriptliner and go over the oils, like you would sign it.
Other options ..... go Pop-art where you write/print the name on a small card and stick it over the fresh oil in the desired spot.
Or you could paint a hot air balloon in the sky (cover the surface with contact paper before you oil paint everything!)
Just some ideas ..... in fact, I really got interested now trying all this myself!! 🙂