from The Century Dictionary.
- noun Same as palatalization, palatalize.
Sorry, no etymologies found.
As for Cyrillic Mongolian, it has some serious imperfections, mostly due to wholesale importation of Russian vocabulary which aren't modified the same way in writing that they are in speech and unlike Turkic, I think palatization isn't so important in Mongolian to require the soft vowel signs.
languagehat.com: YO! 2005
I'm using a superscript "j" here which is the palatization modifier.
The letter form for the approximant Y derives from this palatization mark, as the Y sound is inherent in all palatized consonants.
A "palatization mark" can be added to any of these consonants to indicate that the sound is palatized, or that the middle of the tongue is raised toward the palate, as in "cute", "tune" and "pure".