How did I get my name?

That depends on who your parents are, where they are descended from, and a few other things. In some countries the wife takes the surname of her husband, in some countries she does not, in some countries they hyphenate the two names, in some countries they choose a new name. The children might bear one or both of their parents' names. And they might not. The US census has found at least one family where every member spelled the family name differently.

A child's first name is usually given by the father, or maybe the mother, and that is called a "given" name. It is also called the Christian name, although there does not seem to be any particular reason to call it that.

The name is important since the enactment of inheritance laws in European cultures. Before that time, a husband was not necessarily the father of his wife's babies, and he was not responsible for a baby until he picked it up. That is why we speak of "raising" children. After the inheritance laws it became very important to keep track of who fathered who, and that was when the family name became a reality.

But I have no way of knowing how any of this might apply to you personally.