So what sort of a name is “Heyduk”, and why does it not end with “ski” or “cki”?
Here are the gory linguistic facts.

Hajduk is the standard Polish spelling of the name, though you might also see Chaiduk, Haiduk, Hayduk, Hejduk, and Heyduk (because of phonetic similarities -- all those spellings are pronounced very similarly). As of 1990 there were 9,133 Poles by this name, so it is a fairly common one. People by this name live in all the provinces of Poland, with the largest numbers showing up in the provinces of Warsaw (422), Katowice (1,659), Kielce (579), Krakow (512), Opole (477), Przemysl (312) and Tarnow (453). With the exception of Warsaw (which, as the capital, tends to have large numbers of almost any name you look up), those provinces are in the southcentral and southeastern part of the country, the region called Malopolska (Little Poland).

Names formed from this root are also pretty common, including Hayduczek (394), Hajdukiewicz (930, both of those mean "son of a hajduk"), and Hejduk (1,121), the same name with a vowel change. Hajduk sounds like "HIGH-duke," Hejduk sounds like "HAY-duke," and the switch between what we'd call the long i sound of "aj" and the long a sound of "ej" is very common.

The origin of the name is interesting. It comes from Turkish hajdud, "brigand, ruffian, highwayman," and came into Hungarian as hajdu" (two dots over the u). It came into Polish meaning "soldier in the Hungarian infantry, which existed in Poland from the beginning to the middle of the 17th century, and later served in campaigns of infantry captains." Near the borders Slavs shared with Turks it meant "fellow who waged war against the Turks on his own account." After it became established in Polish it also came to mean "robber, ruffian, highwayman." It also came to be used to refer to servants who dressed like Hajduks, in Hungarian clothing. It has also been used as the name of a dance common among the mountain folk of southeastern Poland, kind of like the dance we've seen the Cossacks do, with a lot of squatting and jumping.

So, the name can mean a lot of things in Polish, most related one way or another to the original Turkish term that came into Hungarian and thence into Polish. It's common in Poland, and I imagine in most cases the connection is with the Hungarian infantrymen -- but in some cases it might have come from the usage of the word as "robber," or even occasionally from the "servant dressed like a Hungarian" connection.