Is it common practice to remove an author's name from a paper? I work as an instructor at a university. I am not a graduate student there and my responsibilities end at teaching. Recently, a supervisor from another department asked me to prepare an article for their department to use, for some extra pay. The subject aligned well with my background and recent research.

When I finished the article, which involved additional research and several weeks of work, I put my name as author, as I would any other paper. After I finished, the supervisor requested that I completely remove my name, as he wished to submit it to the leader of his department, assembled together with some students' work.

Is that at all unusual that someone would request that I remove my name from a paper?
This seems to be a blatant attempt to take credit for your work - as far as I know, this is both not common, nor acceptable. To quote @JeffE "hell, no", or a polite variant, is the only response.

I would, politely but firmly, state that as you have done the research and the write-up, then you are the first author, perhaps offer to have them as a co-author, only if they have contributed something.

I would also consider having a quiet word with the head of the department about this.