There are plenty of great options: Giggs, Scholes, Baresi, Maldini, Facchetti, Puyol, etc.
For me though, the greatest is Francesco Totti. The others above played for clubs who won multiple trophies, and all won the champions league at least once. Aside from a smattering of Coppa Italias and one Scudetto, Totti didn’t win anything with Rome.
For me, it’s easier for a top player to stay at a top club, rather than be a top player like Totti and stay at a club that was rarely considered the best in Serie A. For my money, he is the greatest one-club man of all time.
Who would you choose?
Probably worth defining one club as someone who stayed at the club they became professional at for at least ten seasons or early retirement, rather than strictly one employer. Loans allowed.
If you don’t loosen the definition a bit you’ll find a lot of famous people associated with one club aren’t eligible, because they either got loaned out as a youngster or went to some retirement league at the end of their career.