Fashions might have changed at different times, but my understanding was that babies were named very quickly, precisely for this reason. God wouldn't let them into Heaven unless they were baptised and to be baptised, they had to have a name.
Hmm, it must have been pre-Christian periods I was reading about.
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I would imagine that birthdays would have been celebrated around Saint's days
I figure that was probably the case - if it was St Chronicles' day, there's a good chance of being named Chronicles, and hence whenever it was St Chronicles' feast day those with the name would have an extra celebration.
Though I suspect this tradition may be limited to how Catholic the country was, and would be thrown into chaos by the gloomy Protestants who effectively banned many festivals and celebrations the Catholics had observed.