RM does NOT automatically change a person's display name for adoption, marriage or other legal name change. The Wish List contains multiple requests for RM to use the contents of the various dropdown menus for name type and parent type, but we don't know if that's really going to happen in the upcoming RMv8.
There are a couple options you can use:
1. You could enter the birth name as the display name and ignore any further changes. Clearly you don't like that option.
2. You can add an Alternate Name fact, with an appropriate Sort Date, for each of the person's name changes. This will put a sentence into the narrative for each of those facts. Unfortunately, RM does not use the info in the Name Type dropdown menu to modify each Alternate Name fact sentence. You may not like the appearance of those sentences.
3. You could locally edit edit Alternate Name sentence to resolve the unused dropdown menu selection. That has the disadvantage of being a not-clearly-visible decision in the Edit Person window, and it probably won't survice the GEDCOM eport/import processused to move your file to Ancestry, FamilySearch, etc.
4. You could create a custom Fact Type or use the Miscellaneous fact to insert sentences describing each name change. This might be the most flexible approach, in terms of visibility in the Edit Person screen. I don't know how it will be accepted by Ancestry, FamilySearch, etc.
You mention an [N] variable. RM has no such variable in its Sentence Template Language (see the RM Help for more on that topic). That makes me think your database started out in another program, maybe TMG?