Anytime after the NFL Draft is fine by me. In my experiences, drafts have taken anywhere from a month and a half to three months, so I'd start in July at the latest.
As for a name...
"The Canacuna Dynasty and Those Trying to Catch Up."
It's long, yet catchy.
...I'll think of some more, but I'm not very good with coming up with names.
'CUNA-MANIA IS RUNNING WILD!
"You will be a king here, instead of a peasant at the Cafe."