hi! answers are going to differ by cultures, but you'll find some examples in these earlier threads
Though I can't answer the " when " question I can give you info on how they are used in France ( and certainly other French speaking countries ) since you have not specified any culture you're interested in.
Usually, French people used to give as a middle name the name of the child's godmother or godfather. I don't think there has ever been a law about it but it was a custom.
The first name was generally a " new name " in the family, or the father's/mother's or someone close but could also be the name of one of the godparents. The gender of the name could also be changed according to whom was chosen between the godmother or godfather. See for example : You're a boy named Louis and your godmother is named Jacquette ( pretty old fashion name ;) ) then your parents will certainly call you Louis Jacques. If you're a girl and your godparents are Emile and Louise then you could be named Emilie Louise ( or another spelling such as Louisette ).
That's pretty much it for the common people. Today in France the tradition remained the same but names can also be chosen randomly according to the parents' tastes or to honour someone in the family for example ( I have two middle names, the ones of my grandfathers ).
As for the nobility there is/was a similar pattern of honouring family members and godparents. That's also one of the reasons there has been so many Louis and Louise in the royal family AND nobility.The name Louis was popular for various reasons and after a while since the king was often the godfather of many people there were plenty of little Louis and Louise which at their turn would have kids and godchildren. As an example, Louis XVIII was born Louis-Stanislas Xavier de France. Stanislas was his great-grandfather and godfather ( Stanislas is the French writing of Stanisław Leszczyński, the deposed King of Poland ). There is a saying that this is because/thanks to him that the name Stanislas spread in France.
Maybe someone could enlighten me on this, but I heard that many people ( nobility ? ) in Spanish speaking countries were also given the name of a Saint to protect them ? Such as King Alfonso XII whose birth name was Alfonso Francisco Fernando Pío Juan de María de la Concepción Gregorio Pelayo ?
This of course is not always true for all French speaking countries/places. I know that pre-70s in the Réunion Island people used to have two names. The first one was to be used outside home/family and the other for family environments since the first name was the same as the father ( who in turn had the same as the grandfather,...Etc ). This tradition is not as common as before now though.