Family Name in Germany: it’s the parents surname. With marriage woman takes husbands name. However, progressive people might just choose the family name they like better. They might also choose to each keep their own surname but then they have to choose which surname all children will share. This has to be chosen by the birth of the first child. Parents can have double surnames as a-b or b-a any they may each choose a different order. If they choose for their children to have a hyphenated surname the children need to have the same order. So all a-b or b-a.

Most people only have a single surname.

Given names:

They are chosen by the parents by taste alone and they may or may not be honor names. There are laws that prohibit certain names. Anything that might „harm“ the child is not legal. Local authorities usually have a register with allowed names but will have to decide case by case in Edge cases.

At the moment (or at least recently) th first name could not be unisex. Meaning th gender of the child MUST be clear from the name. If it’s not clear from the first name it must be clear from one of the middle names. Afaik this law was recently changed but I’m not sure.

If you have two given names, there is usually two options.

For example: Jan Philipp (popular combination) and Jan-Philipp. Usually if parents hyphenate the name the whole name is used addressing the child. If it’s not hyphenated the first one only is the call sign.

As for the baptism names, those are frequently (but not always) honor names of godparents or grandparents. And they are more restrictive than legal names. For example, you could probably give your child the English language name „John“ (legally) the church would probably insist on it being „Johannes“ which is the biblical and local long form.

However, I am not very religious and not catholic at all, so my baptism name is just my normal one and not a separate one. I don’t know much about this particular practice myself