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MOS naming scheme

The simplest and most straightforward way to refer to MOS scales is by using the format #L#s, directly specifying the number of large steps (#L) and the number of small steps (#s). This is also probably the most commonly-used format that does not reference the names of regular temperaments. For those who desire more "colorful" names, Graham Breed has proposed the following scheme.

Names for sub-MOS

1L 1s Trivial MOS
1L 2s Happy triad
2L 1s Grumpy triad

1L 3s Happy tetrad
2L 2s bi-equal tetrad
3L 1s Grumpy tetrad

Names for MOS with number of elements from 5 to 10, as proposed by Graham Breed

The logic behind new names is as follows:

Happy and Grumpy are remnants of the dwarf scheme. A good proportion of the shapes fit this pattern, so it's worth having a word for it.
Biggie is a contraction of "bi-grumpy". Rice is named after Rice Kagona.
Bicycle is a contraction of "bi-classical". This family is like the usual fifth-generated one, but half the size.
Mosh is a contraction of "mohajiraish". Mish is related to mosh.
Father is a temperament name. I think the etymology is a pun on "fourths/thirds" and as such names a shape.
Bug is another temperament name, from the draft of the first part of Paul's forthcoming magnum opus. If it's too specific to apply to this family, I suggest "bogey" instead.
"Bi-equal" means the scale is made from two EDOs. There may be a better name for these. They become more important whan you look at complicated temperaments.
I'm using "fair" and "unfair" to distinguish the large from the small.
All the names uniquely specify a shape, and if the number of notes doesn't need to be part of the name it isn't. That doesn't mean you'd leave them this terse in practice.

1L 4s Happy pentatonic
2L 3s classic pentatonic
3L 2s father (sometimes also called: anti-pentatonic)
4L 1s bug

1L 5s Happy hexatonic
2L 4s Rice hexatonic
3L 3s augmented
4L 2s bicycle
5L 1s Grumpy hexatonic

1L 6s Happy heptatonic
2L 5s mavila (other common name: anti-diatonic)
3L 4s mosh
4L 3s mish
5L 2s diatonic
6L 1s Grumpy heptatonic

1L 7s Happy octatonic
2L 6s Rice octatonic
3L 5s fair father
4L 4s diminished
5L 3s unfair father
6L 2s Biggie octatonic
7L 1s Grumpy octatonic

1L 8s Happy nonatonic
2L 7s fair mavila
3L 6s fair augmented
4L 5s fair bug
5L 4s unfair bug
6L 3s unfair augmented
7L 2s unfair mavila
8L 1s Grumpy nonatonic

1L 9s Happy decatonic
2L 8s Rice decatonic
3L 7s fair mosh
4L 6s fair bicycle
5L 5s bi-equal decatonic
6L 4s unfair bicycle
7L 3s unfair mosh
8L 2s Biggie decatonic
9L 1s Grumpy decatonic

Some names of higher-numbered ones

8L 3s Sensi[11]
6L 5s Machine[11]
4L 7s Keemun[11]

10L 2s Pajara[12]
9L 3s August[12]
7L 5s Meantone[12]
6L 6s Hexe[12]
5L 7s Superpyth[12]
4L 8s Diminished[12]
3L 9s Augene[12]
2L 10s Injera[12]

12L 2s Injera[14]
5L 9s Godzilla[14]
4L 10s Doublewide[14]

11L 4s Superkleismic[15]
10L 5s Blacksmith[15]
8L 7s Opossum[15]
7L 8s Porcupine[15]
4L 11s Myna[15]
1L 14s Valentine[15]

6L 10s Wizard[16]
5L 11s Mothra[16]

14L 3s Squares[17]
12L 5s Garibaldi[17]
10L 7s Beatles[17]
7L 10s Mohajira[17]

16L 3s Muggles[19]
12L 7s Meantone [19]
10L 9s Negri[19]
8L 11s Sensi[19]
7L 12s Flattone[19]
6L 13s Hemiwuerschmidt[19]
4L 15s Myna[19]
3L 16s Magic[19]
2L 17s Tritonic[19]

3L 17s Roman[20]

10L 11s Miracle[21]
5L 16s Rodan[21]
2L 19s Tritonic[21]

19L 3s Magic[22]
12L 10s Diaschismic[22]
9L 13s Orwell[22]
7L 15s Coendou[22]
6L 16s Wizard[22]
2L 20s Shrutar[22]

15L 8s Hemikleismic[23]
13L 10s Unidec[23]
3L 20s Roman[23]

7L 17s Mohajira[24]

6L 19s Luna[25]

18L 9s Ennealimmal[27]
14L 13s Octacot[27]

17L 12s Leapday[29], Grackle[29]
12L 17s Garibaldi[29]