Okay, I think there's a misunderstanding of some basics here.
There's a difference between a map name and a map slot. For example, the first map of Ultimate Doom has the map slot E1M1, but the map name 'Hangar'. Two different things.
Now, are you mapping for Ultimate Doom or Doom 2?
If you're mapping for Ultimate Doom, the map slot progression is E1M1, E1M2, E1M3, etc. Ultimate Doom has 4 episodes of 9 maps each, so the highest you can go is E4M9 while maintaining vanilla compatibility. Any of ExM9 entries though are for secret levels so they will be loaded out of order and ONLY if you include a secret level exit on the appropriate map slot for that episode. See this link:
Secret levels aside, as long as you have multiple maps in sequential slots within the same .wad the level switching will be done automatically.
If you're mapping for Doom 2, the map slot format is a bit simpler. MAP01, MAP02, MAP03, etc. all the way up to MAP32. MAP31 can only be reached by a secret exit on MAP15. MAP32 can only be reached from a secret exit on MAP31. Exiting MAP15, MAP31 or MAP32 without a secret exit will bring you to MAP16. Again, see the link above.
Now, for giving your levels names that you see on the intermission screen, those are actually controlled by graphics within the wad. Just make a replacement graphic that spells the name of your level instead of the level name normally associated with that map slot. Then load your custom graphic into your wad with the same lump name as the graphic you want to replace. Maybe someone else can provide a link if I haven't explained this clearly enough.
Lastly, changing the level name on the automap requires another method. The automap level names are hardcoded into the doom engine itself, so the only way to change them in vanilla doom is to create a dehacked patch that renames the levels. I haven't done this myself yet, so maybe someone else can elaborate. If you're mapping for a more modern source port like zdoom you can use the MAPINFO lump mentioned above.
Hopefully this helps!