No, this is not possible. The chapter titles only exist as graphics files in the DVD /Bluray menus.
For real movies, Plex used to be able to fetch titles from chapterdb.org, but it appears this website is down.
Now the only way is to input the chapter titles manually into the MKV files (e.g. with MKVtoolnixGUI )
No, that is always down to your used ripper/compression software.
DVDfab and Handbrake are notorious for embedding those relatively useless titles “Disc#_Title#”” My advice: remove them.
I rip the full movie. If you use makemkv, the resulting file will have chapter markers embedded. You can then go on and compress it in a second step if you want to save storage space.
If you rip a tv show and can’t get the episodes separated, use this guide to split the file on chapter borders [HowTo]: splitting multi-episode files with MKVtoolnix GUI
