Being a brazilian myself, I always got the impression that the portuguese had a lot less variaty of surnames than other europeans.
Some people may think this is too generalizing, but the most common surname in Portugal and Brazil (Silva) is held by 9 or 10% of the population, compared to Smith (1,26% in England), De Jong (0,5% in the Netherlands) or Smirnov (1,61% in Russia). If you take the top 10 surnames of Portugal you have about 49% of the population, while in most contries it hardly goes higher than 5%. Even in Spain the top 10 surnames make just 20% of the population.
So clearly Portugal has very few surnames compared to it's european neighbours, and it doesn't seems to be very related with population size or homogeneity. Why is that?