When I Shecht for Muslims some of them request that I say “bismila a-rahim a-rhaman” which roughly translates as “in the name of the most merciful G-d”. Am I allowed to do this or is it forbidden because of Chukas Hagoyim?

It should not be done, in absence of extenuating circumstances, approved by a Rov.

 

Sources:

ראה שו”ע יו”ד סי’ ד’ סעי’ ז’, פר”ח סי’ י”ט ס”ק ו’, ותבואות שור סי’ י”ט סעיף ח’ וס”ק ט”ו.