Okay, probably in English "given names" would be more specific. In (Swiss?) German we call it "Vorname" and "Nachname", so the names at the beginning of all names and the last name.
Anyway, here is what my genealogy software tells me:
Italy:
- paternal line: ancestor born about 1687 has only 1 known given name, but I don't have his baptism record yet. His wife born in 1695 has 2 given names. Their children have 2-3 given names. Next generation: 2-4 given names. Next generation: 1-3 given names, then 1-2 given names, then next generation (1861-1885) followed a new trend with 1-4 given names (if I remember correctly, the maximum of 6 given names was from around that time in another family). Next generation - my grandfather - still had 4 given names and his siblings 2-4.
What I found interesting in Italy (just speaking for the place where my grandparents were born): the child mortality in 19th and early 20th century was huge, and in some times in some families, the first few children ony got 1-2 given names. When they died, the nextborn got their given names (as children still are named after their grandparents, the given names were repeated until a child survived) plus additional given names, often the names of saints. I assume this should give them more luck and protection.
Switzerland:
- maternal-paternal-paternal line: 2 given names on a female ancestor born in 1810, from their children 3 girls have 2 given names, but all boy have just 1. From their son (my ancestor, born in 1838), his wife has 2 given names and from their children (born 1859-1877), two sons have 2 names and one daughter has 3 given names, all other children just 1. Edit: This line goes back to about 1469.
- maternal-paternal-maternal line: just 1 given name before my female ancestor born in 1843. One of their male children (born 1863) has 2 given names, all other ten children just 1. Their son (my ancestor), again all children have 1 given name, despite my female ancestor who has 2 given names (born in 1904). Edit: this line goes back to around 1550.
- maternal-maternal-paternal line: only one given name in the generations before, then of the children (1857-1870) of my ancestors, all boys have 2 given names and three of five girls have 2 given names and the others just 1. From those children, two males are my ancestors. The one had children (1879-1900) with 2 given names or only 1. The other had children (1882-1909) all with 2 given names and one girl with 3 given names (1897). Edit: this line goes back to 1695.
Germany: earliest known ancestor, father of ancestor born in 1781 has 2 given names, also all his descandants in my direct line.