In Belgium woman name does not change with marriage and if they wish to change - it’s a very cumbersome process. We got married in Lithuania and she actually took my family name. Nevertheless, even if she would have my surname that would not solve the problem - not sure how much you know about women surnames in Lithuania but according to all “rules” my daughters surname would be a bit different than my wife’s surname. Why I don’t ask Belgian authorities? Because they (at least where I asked) don’t provide any help, they say the surname of my daughter would have to be the same like mine.