I know women weren't considered to have professions to the same degree as men and were socially 'attached' to either their husbands or fathers. But at the same time I don't know anyone with the word "daughter" in their last name like "Johnsdaughter" or something, though I believe Iceland/Scandinavia does this with a "-dottir" suffix. So I wondered if there was a disparity in the naming conventions by gender.
It's erroneous to group surname conventions into one "European" group. Iceland uses the father's first name followed by "Son" or "Dottir" to give the surname (e.g. Bjork Godmundsdottir). If Bjork was to marry Arni Henriksson she would still keep her own surname. That system is still in use today although Icelanders are free to choose their own names providing they're deemed to be legally suitable.
In Sweden and Norway a similar system was used patronymically, men were named as the son of their father (e.g. Bjorn Bjornsson) while their wives would be known as being of that surname (Karla of Bjorn Bjornsson). Towards the end of the 19th Century these patronyms became fixed family surnames used in a way that most English-speaking cultures would recognise. Karla would take the surname Bjornsson as would her children. Her female children would take their husband's family surname on marriage.
Across Europe it was also common in medieval times to find surnames that reflected an attribute, profession or place of origin (William le Gros, Charles Cooper, Ivo de Raughton). Again, these per-generation surnames gradually became fixed as recognisable familial surnames, passed down through the male line.
As you can see the male line takes naming precedence in many European cultures. It's interesting to note that this system that "we" (English-speaking cultures) recognise was most common in countries under the see of the Catholic Church. The further one gets from Rome the more likely one is to find differences. It's also worth noting that nowadays it isn't unusual for European women to choose to keep their own surname or for couples to double-barrel their joint surnames in a manner reminiscent of the historical joining of two socially-significant family surnames.
To summarise: we can't describe a single "European" surnaming convention although the majoritative convention across Europe was for women to be named according to their father or male spouse.
Reference:
Beech G. T., Bourin M., Chareille P., Personal Names Studies of Medieval Europe: Social Identity and Familial Structures (2002).