MathJobs has a demo server which is a good way to see what other roles see.
For a letter already written and uploaded, the letter writer can log back in and select the letter from their list:
This brings up a form with various options for the letter. One of them is a text field for "Entry Name":
They can type in something descriptive, and then check the box "allow applicant to see Entry Name". Then click "submit" to save the changes, and confirm on the following screen.
There is a similar "Entry Name" field, and "allow applicant to see" checkbox, when uploading a new letter.
Then as applicant, when you apply for a job that asks for letters, you can click the yellow down arrow to see the list of letters from this writer, and you will see the "Entry Name" description for each one. It looks like by default all letters from the writer will be available to the employer, but you can click the green check mark to unselect letters that are not appropriate.
(As a general comment, whenever you have a question like this, where you want to do something but can't figure out how, I have found that the MathJobs support staff are extremely helpful. I've contacted them a few times with queries like "In my obscure situation, it'd be helpful to be able to do X". Half the time the response has been "Yes, you can already do that, here is how", and the other half it's "That's a good idea, we went ahead and implemented it. See what you think.")