Terry Pratchett played with this idea extensively in his Discworld novels. He used the idea of a 'Metasyntactic variable' (his own nomenclature I believe but open to correction). I suspect it also arose from his early onset Alzheimers. The flexibility of English makes it particularly suited to this kind of usage.
Imagine you do not know, or have forgotten, someone's name, or the name of a thing. A meaningful sentence can still be constructed. 'I met what's-his-name yesterday.' 'what's-his-name' is the metasyntactic variable standing in for the unknown name. One of Terry's favourite was the contraction 'wossname' which could be either what's-his-name, what's-her-name, or what's-its'-name. A very metasyntactic variable.
The L-Space reference here or Google Terry Pratchett wossname.
Who or what the person / object is can be made clear from context but still leave sufficient ambiguity for puns (of which Terry was a master) and humor.
Clearly this is a device for humor in Terry's work, but as with so much of his writting, containing a self deprecating acknowledgement of his own struggle and those with a like condition.
Returning directly to your question, yes.
The use of a metasyntactic stand-in such as Mr Anonymous would be perfectly acceptable but it should be understood as a humorous construction.
Because of the Greek etymology the plural of anonymous is anonymous'. In English this is an awkward construction as is the pronunciation with the double s at the end.
If you had two un-named papers you could go down the route of, 'Mr Anonymous A' and 'Mr Anonymous B'. Or use another Pratchettism and use 'Mr Anonymous' and 'Mr Insert-Name-Here'.
As an academic at a community college I am in complete agreement with @Mari-LouA. No name, no mark. I do however appreciate @Sara Costa's situation.
It may be worth considering however (after appropriate discussion with management) that handing out the odd F to unnamed paper submitters, particularly persistant ones, will:
And yes I am that academic. Cruel but fair.