Most of the shooters in my area that specialize in graduations use "handle mount" flash units on a bracket attached to the camera and powered by an external battery pack. Handle mount flashes were once much more popular than they are now, but they seem to last forever as long as replacement bulbs or heads are available for them. I know one guy that shot my high school graduation 35+ years ago that is still using the same units to shoot graduations today!

These flashes are made to be used in a high volume environment without overheating. They're typically more powerful than camera mounted speedlights and the handle provides space for more/larger internal batteries than most speedlights. Many speedlights can not fire a flash every 2-3 seconds for several hundred pops without a break.

The shooters I've seen doing the diploma shots at graduations all have at least two camera/flash sets for redundancy which they rotate while an assistant swaps the batteries out in the power packs when the graduating class is large enough to need to do that.

One popular unit is the Metz mecablitz 76 MZ-5. It's not cheap, but it is rock solid reliable and will last for many years when used properly. It actually has a cooling fan built in to keep the head cool when used constantly. Note that a "module" needed for your particular type of camera if you wish to use more than single pin manual flash is not included with the flash but may be purchased separately. Ditto for external battery packs and the connecting cables for them.

Sunpak used to be the other major maker of handle mount flashes. It seems most of their stuff is no longer available. Years ago Nikon and Canon used to make some for their cameras as well.

Back about five years ago Chinese "budget" flash maker Nissin offered the 'MG8000 Extreme' that they claimed could go 1,000 pops without overheating (which was longer than any battery pack could power them). It's no longer made, but there are a few new units that surface for sale from time to time. It's not cheap either, as it was a little more than $600 when introduced. It also eats through batteries like a fat kid eats through ice cream. You'll need an external battery pack - no, make that two external battery packs - so you can hot swap them by switching the cable.

If you go with more traditional speedlights, set up at least two camera/flash combos and swap them out every 50 shots or so to let them cool down. Use high quality flashes from first party makers such as Canon, Nikon, Metz, etc. This is not the place to scimp and by cheap Yongnuo flashes. Be sure to get models that have ports for external battery packs and use them. The external packs will allow shorter recycle times that you'll need to keep up with the line getting their diplomas.