What is the name of the maximum training level setting?

You can change the values of your player character's skills using modpcs (modify player character skill), and change their attributes using modpca (modify player character attribute).

They are used like this:

• modpcs <SkillName (without spaces)> <value (0 to max. 255)> (e.g. modpcs sneak 120)
• modpcs <AttributeName> <value (0 to max. 255)> (e.g. modpca intelligence 80)

The alternative is using player.setav <attribute> <n>, which works for both attributes and skills.

The difference between the two approaches is how they are taken into account when leveling up your player character: setav counts directly towards levels (increasing a skill this way will advance your level like a 'natural' increase would do), whereas modpc will "technically give you negative progress towards your next skill increase".

I read your question as asking for a way to allow the game to keep leveling up your PC after the vanilla limits (of 100) were reached - tweaking the ceiling, so to speak, without changing the actual values. So, just to be clear, these commands don't only change the maximum level allowed, but will set it to the given value.
For targeting skills (and attributes) specifically however, they seem to be the best option you have (as using advlevel, setlevel <n>, or advskill <skill> <n> has more serious drawbacks).

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