It may be helpful to look for info on others with the same surname. There is an Anyzek family in Camden in the 1910 census, headed by WalentyValentine and including brothers Joseph and Philip. They are all about the same age as Stanislaw, and he may be a fourth brother.
I couldn’t find Stanislaw’s immigration record, but here is Walenty’s:https://familysearch.org/ark:/61903/1:1:JX21-5PR
It gives his mother’s name as Tekla and also lists his hometown: Hedozymysl(?)
If any of the brothers married in New Jersey, the marriage record should include parents’ names. Unfortunately, the record for Stanislaw’s 1905 marriage in Philadelphia doesn’t include parents.