For knots with 10 or fewer crossings, KnotInfo uses the classical names. For knots with 11 crossings, the naming convention is that of Dowker-Thistlethwaite, as used by Knotscape.
Early tabulators named 11-crossing knots as well; for instance, the 11-crossing knot called "11a367" in Dowker-Thistlethwaite notation is listed as "1" by Tait and "(11)" in Conway notation. These efforts culminated in Conway's enumeration, polished by Perko.
The Conway names list in KnotInfo is most relevant for 11-crossing knots.