After looking at navel ranks, yeoman isn't a rank, so I am assuming it isn't an actual rank in Star Trek either, but instead a function like engineer, chef, etc.
What does a yeoman do? And what kind of rank do they carry if any?
In the US Navy an enlisted person's rank is a combination of their "rate" (petty officer 3rd class, petty officer 2nd class etc) and their "rating," which is their specialty. A yeoman starts out at Yeoman 3rd Class (petty officer 3rd class, pay grade E-4) and can go up to Master Chief Yeoman (master chief petty officer, E-9). They can even go up to warrant officer rank, at which level the specialty is called "ship's clerk."
In the TOS episode "Charlie X" Tina Lawton was introduced as "yeoman third class," which sounds very much like the USN usage.
In the US Navy the yeoman rating handles administrative, clerical and secreterial duties, correspondence, record keeping, etc.