No, COM files had no header. [2] I think that's part of why they were replaced. ZM was for EXEs. I think that one was someone's initials. (Yes, looked it up. [1])

I think what parent is remembering were characters that effectively created a jump instruction at the beginning of the file.

[1] https://en.wikipedia.org/wiki/DOS_MZ_executable

edit: [2] Section 6 of the paper talks about that, just noticed.