Shouldn’t it be “Abd-a-Rahman”?
According to vague memories of 7th-grade Arabic, you should drop the “L” before an “R.” Or am I wrong?
Are we transcribing or transliterating? The former reproduces sounds, the latter reproduces orthography on a one-to-one basis. They’re not the same thing.
Besides, the “sun letters” like r don’t make the l of the definite article disappear–it assimilates, making for a doubled rr. In pronunciation, but not in spelling.