Kefla's SSJ2 form is indeed not your regular SSJ2. This is because a lot variable factors are used which we should keep in mind. These are caused by the fusion of 2 Saiyans with different forms. Kale is using her Legendary/Berserk SSJ forms which emit a green aura. These forms bring a close to infinite pool of power and ki. Caulifla on the other hand is able to utulize SSJ2 pretty well. This form can be recognized by the lightning sparks and the violent aura that covers the whole body and clothes. SSJ itself has a rather calm aura without any lightning sparks, with ofcourse almost the same hairstyle.
Now to get back to Kefla in the screenshots you provided we can see 3 important things.
- Green aura (Kale's LSSJ/BSSJ)
- Lightning sparks (SSJ2 in general)
- Violent covering aura (SSJ2 in general)
So with these observations it is safe to assume that the most accurate name to this form would be LSSJ2. This is because Kale was able to master her BSSJ, making it the LSSJ. This in combination with the SSJ2 from Caulifla delivers us the breathtaking LSSJ2.