蒙 is second tone (méng) in the common meaning of "to cover / ignorant / to suffer (misfortune) / to receive (a favor) / to cheat"
蒙 is third tone (měng) in the also common meaning of related to Mongolia / Mongol ethnic group.
That much I can handle.
The second meaning of 蒙 is also pronounced as second tone (méng) in Taiwan, same as the first meaning. I like Taiwan's way more, having only one pronunciation, but since the mainland doesn't do that, I need to remember both.
蒙 as second tone (méng) is the one used for surnames.
Still OK. Now things get even more complicated
蒙 is also the simplified form of 濛, which means "drizzle / mist". Fortunately, it is also pronounced as second tone (méng).
蒙 is also the simplified form of 矇. 矇 itself also has two pronunciations, second tone (méng) meaning "blind / dim sighted", and first tone (yes!) (mēng) meaning "to deceive / to cheat / to hoodwink / to make a wild guess". From what I can tell (corrections anyone?), for this character the first tone (mēng) is the more common one, and the second tone (méng) is seen only/mostly in the word 矇矓. And as a surname.
Ouch, my head hurts.
MDBG also lists a first tone (mēng) meaning for 蒙, meaning "(knocked) unconscious", but I don't see any words that use it, so I have to conclude it is obscure or an error, and I will ignore it. [Taiwan MOE dictionary confirms this, and has only a single pronunciation for 蒙.]
Speaking of errors, MDBG also lists the pronunciation of 蒙嘉慧's surname as third tone (Měng), even though the other entries only list a second tone pronunciation as a surname. Error? Or exception? How does one find out how people pronounce their name?