You left out the best bit: while the convention is that males use patronyms and females matronyms, you can choose which parent you want to honour with the -nym; you could also be Luke Padmesson or Leia Anakinsdottir if you want.
Also just to point out that for many places, surnames are a relatively recent thing for most social strata. Patro/matronymics predate them in almost every part of Europe, and in many places surnames started out as patronymics. This is why you have all the surnames ending in -son/-sen in the UK and Scandinavia, -ex in Spanish, -vich (or a variation thereof) in Slavic languages, Mac- in Gaelic, O’- in Irish etc. All these are patronymics that predate the use of surnames.
Plus, the arrival of the surname is a very recent thing in many parts of Europe. In the Nordics, only people belonging to the estates (so nobility, clergy, bourgeoisie and land-owning peasantry, a small minority of the total population) had surnames before the 19th century. The vast majority of people would only have a first name, using either patro/matronymic (or in Finland the name of the house or village where they worked and lived) to distinguish themselves from those with the same name if needed. In Finland, people have been required by law to have a surname for only a century (exactly: the first law on surnames came into effect in 1920). Iceland never did that.
And ultimately, why should they? A surname is just a convention that people have at some point decided on – and one that emphasises your patrilinear family over you as an individual and the rest of your relatives.
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