When I taught Maths at an FE college, we'd have between 200 and 250 new faces and names to learn each September. In the first session of the year, to introduce ourselves, I'd play Getting to Know You with them, along the lines of
"Hi, I'm Tim, and I like playing guitar <I mime playing guitar>"
"Hi, he's Tim <points at me>, and he likes playing guitar <mimes playing guitar>, my name's Rob and I like meeting da laydeez <pelvic thrusts, to my feigned disapproval>"
"Hi, he's Tim <points at me>, and he likes playing guitar <mimes playing guitar>, his name's Rob and he likes meeting da laydeez <pelvic thrusts>, my name's Sam and I like standing in the middle of fields <mimes standing in field>"
etc...
Because I'm nice I only got the students to introduce the 10 who'd come before them (i.e. the twelfth would start with Rob and the thirteenth with Sam). I'd only allow two people in any one group to select the same activity as their chosen pastime (otherwise they'd all be playing on games consoles, playing football or shopping), and we got some REALLY funny ones over the years (those above are genuine).
I'd quite easily be able to reel off all 20-25 students in a group afterwards (and their activities), and I'd only need the occasional reminder in week 2 (the ridiculous timetabling meant that we only saw each group once a week, for 90 minutes!)