Rafiq
In one of his conversations with Malik at the Assassin's Bureau in Jerusalem, Altair addresses Malik as "dai" (during the Majd Addin assignment.) The dais are the direct representatives of the Imam, who is the exalted spiritual leader of the people. This means that Malik was made a dai after he pulled off the task that Altair failed to accomplish in the beginning. In the beginning of the story in the cut-out scene under the Temple, Altair states that he is of a higher rank than Malik. Altair is a Master Assassin Instructor, which means that Malik is not yet a dai. While devising a plan on how to approach Al Mualim, Malik refers to Altair as dai (Al Mualim assassination) showing that he obtained the rank upon taking Roberts life.
The Bureau leaders in Acre and Damascus are rafiqs. That is not their name but their rank. A rafiq is a first level instructor just beneath a dai. Initially they are teachers and field contacts that provided Altair with where and when to best strike. But after Altairs major failure, Al Mualim places him under the entire Asassins Order. This results in rafiqs obtaining authoritive power over Altair. Rafiqs are then authorized to grant or deny the carrying out of a assassination strike, if Altair does not posess what they feel is enough information on the target. Once Altair has properly learned where and when the target will be, he is granted permission to perform the strike. But only after receiving the assassination feather marker.
Each of them has a particular skill or talent which he may teach in addition to teaching philosophy, the Quran, and the Creed. Malik is a cartographer, or map maker. One of the rafiqs is a potter (Damascus) and the other is a scholar/scribe (Acre). Their given names are never said. They are only called rafiq as a title of respect.
The higher level teachers at Masyaf (village and fortress) are those who wear the white robes with a black djellaba. Al Mualim also wears this attire.