Auvaiyar is one of the most famous poet in Tamil Literature. But has there been only one Auvaiyar ? I still remember when I went to cast my first vote for election in Chepauk, I saw two candidates with identical names, and the name was M.Karunanidhi. I also heard there were several people named Vijayakanth standing in the constituency where Vijayakanth was standing. So if some one is popular there are surely going to be impersonators with the same name. This trend can be found in Tamil Literature too.
Just fyi, in the US it is illegal for two candidates to go by the same name for the same exact reason that it confuses the public, even educated public. There were probably several Avvaiyaars, we don't even know if Avviayaar was really male or female if I remember right. Same with Valluvar (I mean probably one person who wrote the kural but no furthe idea if he was male/female and what was his religion). Scholars please comment more, but this is often taught in school - I remember learning it as far as 9th grade.