The surname has three ancestral areas I know of for sure, and possibly a fourth one, each in a different area.
1. A Jewish surname in the area near the mutual borders of Poland, the Czech Republic and Germany, in parts now mainly Polish, in Silesia.
2. A German, mainly Lutheran surname, centered around the coast of the North sea.
3. An English surname, thought to be a variant of Peck, mainly Methodists.
4. A distortion of sefardic Pico, originally from Catalonia, Spain (conjectural, I have seen no proof).
---------------------------------------------------------------------------------------------------------------------------------------------------
Balázs Déri says :
Some of these Pick families as well as Pikey travellers in Brittania may be related to Pik-Raj tribe of Iranian Gypsies who might once have belonged to Rajput cast .
See Rajput,Zigeuner,Alexander,Trenka,Purecse,Cifut,Inca,Arauco,Rakowitz,Katscher, Czitrom,Czinka,Wilczek,Chile,Rothwalsch,Horpácsi,Horpatzky,Petry and more !