Where does “ترجمه” come from?

ترجمه (Chagatai) comes from Classical Persian تَرْجُمَه, from Arabic تَرْجَمَة — translation.

Ancestry of “ترجمه”, step by step

Step	Language	Word	Meaning
1	Classical Persian	تَرْجُمَه	—
2	Arabic	تَرْجَمَة	translation