I think this is over simplified.
Before X time in most European countries and probably in many other countries that I am not familiar with, the only birth related records were baptism or equivalent naming ceremonies. The ordinary people were illiterate.
We have no idea what names were used by family members, friends or neighbours. Many times we probably don't know exactly what language the local people used. There were in many locations local dialects, the records were not written in those dialects, they were written in the language used by the only literate people, the church officials.
For most people prior to required government records the only times their names appeared are in written church or religious records, baptism, marriage and burials.
I have a good friend who was born in Holland, the first name on his baptismal record is Lambertus. In high school his friends called him Bert, his mother called him Lambert. His sister called him Lamie.
Another friend has the same official first name as his father, some of his uncles and several cousins, they all have Wayne as a first name.
He decided it was too complicated to use Wayne as his usual first name, he decided to use his second name Steven.
In high school he got called Slash, as the name he used was written on school documents as Wayne/Steve.
If I look for records for Steven, with his last name I won't find any, and I certainly won't find any records for Slash.
Whether we like it or not, records use the name used on other records, not what other people may have called the person.