I would like to share my observations after many years of genealogy work regarding giving names to children at the baptism. There were four main ways of choosing the Patron Saint. Yes, in 19th century the most important was giving the name of the Saint who was popular in Poland or in the area.
1. If a child was born around 4th of October they would be named Francis because 4th of October is St Francis memorial. Children born around December 24th would have names Adam or Eve etc.
2. Very often people were giving the names of Patron Saint of the parish. E.g. in St Stanislaw parish lots of boys would have the name Stanislaw.
3. There was a general not written rule that children had names of their grandparents
4. Children very often had names of their Godparents
Of course many parents were choosing the name they liked and it was not always connected with any of the above mentioned rules.

