Is 'r' in Br/Amr pronunciation of 'Arjmand' (Persian word) silent?
(In other words, how is this word pronounced in Br/Amr English?)
It depends whether or not you are speaking American English or British English.
American English uses the rhotic 'r', while British English 'r' is non-rhotic.
For example, rhotic speakers say "barn", and 'r' has a strong nasal sound, whereas non-rhotic speakers say "barn" pretty much like "bahn".
So "Arjmand" could be pronounced "Arjmand" or "Ajmand"
Well, this is actually a bit of a misguided question, as that isn't even how the name is "spelled" in Persian. They have their own alphabet. If someone decided to write the word as
Arjmand, they presumably picked the letters for the benefit of English speakers, and presumably meant it to be pronounced roughly as written.