A polish or german name with others derivations as Stigar, Sztigar, Sztygar, Estigar, Estigara, Stigara, Stigare.
Stygar probably is a variant of Sztygar, a word meaning "foreman," especially in mines. This term comes from German, and is comparable to the German names Stieger, "one who lived by a mountain path," and Steiger, literally "climber." So this could be the German name rendered in Polish spelling, or it could be a Polish name from a Polish word borrowed from German. Either way, the ultimate origin is German. The form Stygar is most common in Poland -- as of 1990 there were 310 Poles with that name. The largest numbers were in the provinces of Krosno (126) and Rzeszow (29), with smaller numbers in several other provinces, mostly in southeastern Poland, which is quite mountainous.
Derivations names Stigar, Stygar, Stieger, Steiger, Astigar, Estigara.