What are the best practices to anonymize user names in data? I'm working on a project which asks fellow students to share their original text data for further analysis using data mining techniques, and, I think it would be appropriate to anonymize student names with their submissions.  

Setting aside the better solutions of a url where students submit their work and a backend script inserts the anonymized ID, What sort of solutions could I direct students to implement on their own to anonymized their own names?

I'm still a noob in this area. I don't know what are the norms. I was thinking the solution could be a hashing algorithm. That sounds like a better solution than making up a fake name as two people could pick the same fake name.possible people could pick the same fake name. What are some of the concerns I should be aware of?
I suspected you were using the names as identifiers. You shouldn't; they're not unique and they raise this privacy issue. Use instead their student numbers, which you can verify from their IDs, stored in hashed form. Use the student's last name as a salt, for good measure (form the string to be hashed by concatenating the ID number and the last name).