How can I tell how many damage dice to roll for an NPC's cantrip?

Question

For PCs, cantrip damage increases with their total character level and not their class level (see this question for reference: Do Cantrips use your character level or class level?).

However, NPCs do not normally have class levels, and their stat blocks don't state a total character level.

How can I determine the number of damage dice to roll for an NPC's cantrip?

1. Should I use their number of hit dice as their total character level?
2. Should I use their stated Spellcaster level? (What if they don't have one?)
3. Some other method?

A couple of examples to illustrate my concern:

• An Archmage (SRD p. 395) has 18d8 + 18 hit dice and is an 18th-level spellcaster, so methods 1 & 2 here would produce the same result.

• Nezznar the Black Spider (LMOP p.59) has 6d8 hit dice and is a 4th-level spellcaster, so methods 1 & 2 would produce different results.

  The fact that Nezznar has more hit dice than spellcasting levels implies to me that Nezznar has, in some unspecified way, multiclassed - and that 6 would be his total character level - and the number I should use for cantrips, not 4 (his spellcasting level).

A good answer would also cover NPCs with Innate Spellcasting and no spellcasting level. See, for instance:

• A Green Hag (SRD. p 319) has 11d8 + 33 hit dice but no spellcasting level listed.

Answer 1

Spellcasting

For the Spellcasting trait, you use the listed spellcaster level as read on page 10 of the Monster Manual:

The spellcaster level is also used for any cantrips included in the feature.

This means an archmage is treated as level 18 for the purposes of cantrips, and Nezznar is treated as level 4 (despite his greater number of hit dice).

Innate Spellcasting

Innate Spellcasting will sometimes list a specific level (in which case use that one), but otherwise you use the monster's CR (as also stated on page 10 of the Monster Manual):

If a monster has a cantrip where its level matters and no level is given, use the monster's challenge rating.

For the green hag, this means it is treated as level 3 for its cantrips.

Answer 2

You choose the level in the following order:

1. Is a spellcaster level given? If so, use that level.
2. Use their challenge rating.*

*For reference, see MM, p. 10:

If a monster has a cantrip where its level matters and no level is given, use the monster's challenge rating.

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You state:

The fact that Nezznar has more hit dice than spellcasting levels implies to me that Nezznar has, in some unspecified way, multiclassed - and that 6 would be his total character level - and the number I should use for cantrips, not 4 (his spellcasting level).

Do not confuse monsters with player characters. Generally, NPCs don't have classes the way players do, nor are they limited by what is available to player characters.
Therefore, even if an NPC/monster is listed as a "Xth level spellcaster", that does not in any way mean they have any other similarities to player classes. A monster that is, for example, a 5th level spellcaster with access to cleric spells (--> Bone Naga), does not also gain any cleric features of that level.

Therefore, since nothing states that hit dice = level, this value can't be used for cantrips. In fact, that's not even a clear rule for PCs - that players gain one hit dice of HP per level is listed explicitly in every classes' description. (Yes, it's effectively a rule, but not class-independent as per RAW)