I have a sheet that I auto filter by job title, i.e. Doctor, Nurse, Tech,
Admin.

With no auto filter on, the each person list listed by name, with the column
next to their name designating them as 1 through 100.

If I auto filter for, let's say Nurse, of which there are 35, what formula
can I put in the cell to the right of the name to number these people as 1
through 35?

In other words, the number would change depending on which rows were visible
at the time.

The names on this list change on a regular basis.