In Sweden, until the 20th century, they used the patronymic system of names. That meant that Johanna, whose father was Johanes was called Johanna Albertina Johanesdotter. Even when she married, she used the last name of Johanesdotter. Her husband, Johan, whose father was Anders, went by the last name Andersson. Their children used the last name Johansson or Johansdotter.
It actually makes it easier, not harder to trace family members – so long as you are doing only one generation at a time. There is no such thing as searching for all the “Smiths”.
Unfortunately, they also used various other forms of names, such as where they were from (such as Carl from Terrace), or what they looked like (for example: John the big).