There is probably no rule of thumb which covers whether student photos need to be displayed in quiz apps autosuggestions.
There are rules of thumb which say that it's best to provide helpful and relevant information.
The main purpose of the autosuggestion list is to let users easily locate the items they're looking for, without having to type them out. It can also help users pick one of a few identical items or discover items that may be relevant to their search.
You need to ask yourself whether the faces provide any added value, and what's the price you're paying for displaying them.
For example: are you users familiar with the students? Will they recognize faces faster than they'll read the names (humans usually do)? Do the faces provide information which might be relevant even for unfamiliar users, and it's not covered by the name alone, such as gender or age?
And it terms of the price you're paying - will displaying faces slow down your performance? Will it mean that fewer suggestions can fit in the autosuggest box? Will it clutter or overload your UI?
The same goes for any other information you're considering to include in your suggestions.