A slight edit on what Leo suggests, but rather than repurposing the Layout Name token, for single player parts instead just use {@playernames@} for the ISMN. Doing this keeps your Layout names and is an easy add to master pages.
Single player parts: https://imgur.com/07pQ8aB
For full/vocal scores or multi-player parts, the ISMN token will have to be {@layoutname@}. For a full score/vocal score this is easy, because usually the first page doesn’t include any kind of layout name anyway (unless you’re using the layout token to say “Full Score in C” or “Transposed Score” or something). Additionally the layout name is usually never in the header either.
Full Scores/Vocal Scores: https://imgur.com/Cgskz13
For a multi-player part which needs to show a layout name on the first page or the header, this is slightly tougher. I’d use either {@playernames@}, {@playerlist@}, or {@stafflabelsfull@} for the layout name on the first page, if you don’t mind showing every instrument. Otherwise you’ll have to do some kind of override either for the layout name or the ISMN. For the header, if you need a short layout name rather than a whole player list you’ll simply have to make a new master page based on default for that one layout.
Multi-player Parts: https://imgur.com/JnbDR1R
Not 100% perfect, but at least this way the only layouts which will appear in Dorico with its ISMN as the layout name will be full score layouts and multi-player part layouts. Any file should likely only have a max of two full score layouts — full and vocal score. You can arrange the full score layout at the top and vocal score layout at the bottom so the numbers don’t become confusing. And then it’s just a matter of how many multi-player part layouts you have (the max I’ve ever had is one — percussion score, but YMMV)