If they said they're doing the printing, then presumably you'll just need to provide them the digital files, in a pixel dimension that will print nicely at 4x6. 1200x1800 is appropriate. Make sure to leave some safety space on the edges of the photo (read: don't crop too tight), so it can be placed in a frame. You may need to provide them with a print release; some local printers (Walgreens etc) might refuse to print professional-looking photos without proof that the photographer has given them permission/license to print.
It's somewhat unlikely that you'll need to keep track of who's who in the photos. If you're giving the company the files to print, presumably their representative will be able to figure that out, unless it's a REALLY large company. How many subjects we talkin' about here? If it's under 200 employees attending, their event planner will know how to distribute the photos to the right recipient... and it's up to the event planner to print multiple copies of the group photo, if they so desire.
If you feel you MUST keep track for yourself, here are two solutions:
1) Have a whiteboard on which the subject writes their name. Take two shots of each subject: one with them holding the whiteboard with their name on it; a second "regular" shot. Pros: No paper to lose; no way to get mixed up or out of order. Cons: gotta take two shots of each person, and the first shot kinda feels like a police line-up shot.
2) Have a piece of paper, write down the file number and the subject's name for each shot. Pros: Simple, easy to understand. Cons: Easy to get mixed up, accidentally skip people, etc. Easy to lose the paper.
DON'T just keep a paper list in numeric order without any reference to the file number. If you skip a person or take two shots of a person, or people get out of order in line, then your paper is worthless.
It's going to be tough for us to give you any more instruction; honestly, you'd be better off getting clarification from the person who's responsible for planning the event for the client. If they're doing the printing and distribution, it's all on them.