Czech (his passport) changes endings all over the place. It's how our grammar works. Nouns and adjectives have different endings depending on their contextual gender associations. Czech last names are either adjectives (rarer), in which case the male form ends with ý and the female form ends with á (the latter generally denotes femininity), or nouns, in which case the female form gets turned into an adjective with the ová ending. For example, if your last name is Kovář == Smith, your wife's or daughter's last name would be Kovářová, which could be loosely translated as "of Smith" or "of Smith material" (Kovářka would be the Czech noun for "a female Smith", but female noun surnames don't turn up in formal Czech -- though they make reasonable abbreviations/nicknames among friends). Czech has also the very similarly sounding ova ending (as opposed to ová) which literally denotes possession in addition to the female gender (Kovářova == a (male) Smith's). This doesn't turn up in Czech last names, but it does in other Slavic last names (notably in Russian last names), which makes it sound familiar. Whether it also denotes possession in those languages, I don't know.

Only the endings, for example the feminine form of Novák becomes Nováková. When moving to a country where there's no distinction, one usually stays by the masculine form in the official documents, regardless of gender. For example, an American-born daughter of Polish immigrants inherits and uses Kowalski as her last name, but if she were born in Poland, she would use the form Kowalska (and her son would be called Kowalski, etc.)

If you come from a place where you surname is simply FathersnameSon or FathersnameDaughter, then yes. Eg: Bjornson or Einarsdottir (sorry Scandi friends for typos)

Yes, exactly, in fact I thought he has been caught because of that, not about the credit card thing...

Reference: https://en.wikipedia.org/wiki/Czech_name#Female_surnames

Exactly but not for all surnames. See: https://www.quora.com/Is-it-true-that-in-Russian-culture-a-w...

First names, too, see Valērija/Valēris in Latvian (male names -s, female names -a). Same for family names.

After we were married, my wife's family name changed to 'match' my non-Latvian name, and our son got a different family name on his LV passport. e.g.

    John Smith <-> Jana Smitha
                |
                v
    Josefs Smiths/Joseph Smith

We use the LV passports for primary ID, which sometimes causes some confusion when setting up family accouts etc. with non-passport-control staff.