This family name came most probably from the name of the shtetl that was inhabited by the family before it received the name. Taking into account that in the 19-th century people with this family name are encountered almost exclusively in the Grodno gubernia, the shtetl must have been there.
Already in 1838 one finds mentionings of Leiba son of Abraham, Heshel son of Leizer, Itzko son of Iosele and Yankel son of Chaim Pitkovskies among the residents of the shtetl Ruzhany, in the Grodno gubernia.
Later one can find Pitkovskis also in other regions of the Grodno gubernia - in the shtetles Slonim, Zelva and Pruzhany and in the towns of Brest and Byalistok.
By the beginning of the 20-th century Pitkovskis reached Saint-Petersbourg. Pitkovsky Moisei son of Pinhus who was born on 15 of June 1897 studied in the private Jewish male gymnasium of Eisenbet in 1915-1916.

The following story from the Jewish Encyclopedia of Brokgauz and Efron of the beginning of the 20-th century is interesting:
"Not too long before the Passover of 1657 a body of a Christian child was found in the Jewish quarter of Ruzhany, a "victim of the Jewish bloodthirstiness" as rumours said. The masses were ready to attack Jews but the owner of the shtetl did not allow the pogrom saying that the Jews under suspicion will be judged in court. Two and a half years passed and the "incident" was forgotten; possibly the Jews were found not guilty by the court."
According to the author of the introduction to the book "Daat Kedoschim", Jesuits did not give Jews a possibility to ask at the king's court for a lawful consideration but gave the "incident" at the peasants decision. According to another version bourgeois who were hostile to Jews on the base of economical interests used the absence of the shtetl owner in 1659 and judged Jews on their own.
The legend says that in the day of Rosh-ha-Shana masses attacked the praying Jews threatening to kill them. The court of bourgeois accused all the community of a killing with ritual purposes and offered to give as victims two members of the community. Rabbi Israel ben Shalom and rabbi Tobiya ben Joseph were chosen (possibly they agreed to this martyrdom by themselves). On the second day of Rosh-ha-Shana they were executed.
Rabbi Israel's son, rabbi Simon described this tragic event in a moving "sliha" and besides composed a prayer "El Male Rehamim". Until today the memory of the martyrs is respected among Ruzhany Jews. Every year on the second day of Rosh-ha-Shana they put a candle in the synagogue for the memory of the martyrs and on the Atonement Day they recite the above prayers. A legend says that the two martyrs before the execution blessed the Ruzhany Jews and promised to ask G-d so that Jews face no more false accusations of killing. On the local cemetery there is a stone monument in the memory of the martyrs (that was restorated in 1875)"