I rename players every draft and for the 7 round drafts, the only issues would be the name not in the name machine, or it's spelled wrong, and once I got "that name is already in use".
In the 2 recent allocations, you can rename everyone during the draft, but the second it's over you can only rename rookies up to the time training camp sim begins. That's why I had to name John Madden real quick, being the next to last pick.
Post draft, any rookies signed before camp may also be renamed up to the TC sim.