LeBron James has the most games in the NBA Finals with 10+ assists, 10+ points and 10+ rebounds, with 11 games.

most nba finals games with 10 point and 10 assist and 10 rebound or more
Interpreted as:
most NBA finals games by a player with 10 or more point and 10 or more assist and 10 rebound or more
LeBron JamesLeBron JamesNBA Finals1132012313544.729.112.311.
Magic JohnsonMagic JohnsonNBA Finals81301189242.616.311.514.
Draymond GreenDraymond GreenNBA Finals337334042.012.313.311.
Jimmy ButlerJimmy ButlerNBA Finals275242346.037.511.512.
Larry BirdLarry BirdNBA Finals254232645.527.
Walt FrazierWalt FrazierNBA Finals225222441.512.512.011.05.511.547.81.53.542.9837
Wilt ChamberlainWilt ChamberlainNBA Finals226207148.513.035.510.
Bill RussellBill RussellNBA Finals242204948.021.024.510.
Kevin DurantKevin DurantNBA Finals120101237.620.
Stephen CurryStephen CurryNBA Finals132111036.332.
Rajon RondoRajon RondoNBA Finals119101242.
Tim DuncanTim DuncanNBA Finals121102046.
Jason KiddJason KiddNBA Finals123101043.
Charles BarkleyCharles BarkleyNBA Finals132101246.
Scottie PippenScottie PippenNBA Finals115121242.
James WorthyJames WorthyNBA Finals136101644.
Dave CowensDave CowensNBA Finals125102148.
Wes UnseldWes UnseldNBA Finals111102339.
Elgin BaylorElgin BaylorNBA Finals113111245.
Jerry WestJerry WestNBA Finals142121348.
StatMuse has game-level data for assists going back to the 1960 Finals.