As a general rule, you cannot show the "many" side of a one-to-many relationship like this on a list view on the "one" side. Why? Because there's many values, and it's not clear what the right way to show that would be in a list view context, where what you expect is one row per record. Salesforce doesn't have native modeling for one-to-one relationships.
Note that you can do this in a report, and you'll get what you might expect if you have SQL joins in your head - as many rows for each Mentor as that Mentor has Mentees, with the Mentor information repeated for each Mentee.
If what you're working with is actually a one-to-one relationship (i.e., each Mentor will only ever have one Mentee, full stop), you can use a Process Builder automation. You'd attach it to the Mentee object, and configure it to update a "Mentee" link on the "Mentor" every time the Mentee is updated. Then you'd actually have a field on the Mentor that you can show in a list view.
Contrariwise, if what you have is more like a many-to-many relationship, it may be that the right data model for you is a junction object: a record representing the match itself, with master-detail relationships to both the Mentor and the Mentee. Your list views could be built on this Match object, and would show the details of both Mentor and Mentee - as well as any other metadata you chose to add to the match, like its active dates or status.
Keeping the data model you have and not treating it as one-to-one, the only route I can see to get this information in a list view is to use Declarative Lookup Rollup Summaries to populate a Text field on the Mentor with a concatenated list of Mentees' names. You can do this with a rollup in the "Concatenate Distinct" mode.