Random Picker
The college has a subscription to Triptico Plus, which has some funky tools, including tools for randomly selecting people from a list, as of June 2021 they have significantly overhauled their site, now it's much easier to use, and works on any device, if you don't have an account to access, contact IT Support.
So, this random-name-picker site, is a lot less cool to look at but more than makes up for that due its sheer simplicity, no log in needed, just load the bookmarked page, like these: