Carrier did not do a "naming rights deal", they provided a gift and the facility was named after them. Just like when someone donates a lot of money and gets their family name on a library, or Chem lab, or basketball practice court.
This fact has been posted in practically every single thread about the name of the Dome, maybe it needs to be stickied at the top? Because it's kinda important.
And AFAIK the first true naming rights deal was Schaefer Stadium in 1971. But I may have missed one prior to that.