Not going with correct pronunciation anything.
In America, if you are guessing, you go by the old schoolyard..........
slap-you-silly-if-you-insist-on-a-squirrely sounding name for generations.
Tree-mont or Tree-mo will both get you by at fourth grade recess anywhere in the USA.
Sounds like a funny tree maybe, but its a stretch to make much fun of it.
Trem (bly) O
or
Try (harder)-mo would both get you smacked around like a rag doll.
My family name on my mother side was originally Fellowes, back before the revolution.
Could maybe get away with that prissy in Connecticut/Maine or somesuch,
but take it down south for a couple generations?? Yeah, right !
It turned into Fellers, as in ..........
"Them Fellers down on the corner."
This is how my uncles and cousins sign their name to this day.
yours Scott