PS - so yeah, it's phonetic, Sinbad . . .like the pirate.
Actually to be really pedantic it's Sinbad the Sailor. As-Sindibād al-Baḥri was a sailor not a pirate. From Basrah.
Most Westerners are familiar with him from translations of The Thousand and One Nights where he has been included in the tales of Scheherazade but historically the Tales of Sinbad were not part of the Thousand and One Nights.