The argument I would have is that this individual would have to be the best in the business (at least in the conference) for a decade or more. That if you ask who's the best coach, it's that individual with 90% or more agreement across the board from every fan base out there.
Some people that would qualify, IMO, have bounced around, but there aren't many of those. Rick Pitino is a legend IMO.
To take Tennessee folks out of the discussion, Vince Dooley is not a a legend. Shug Jordan is not a legend. Pat Dye is not a legend. Kirby Smart will eventually qualify (don't know if he has been around a decade).
The #1 obvious answer for Tennessee is Pat Summitt. Clearly a legend.