You’d rather change your name instead of giving the child only the name of his/her father?
It’s been the case for decades here, and we never had any problems. If my parents had given me their full names, I’d have 4 last names like in the example you have mentionned. I only have one because my parents knew it would be too long, so I only kept the name of my paternal grandfather. They chose one this way.
My aunt, who was born and lived the most of her life in France, had taken the name of her first husband. When she arrived in Quebec, she was a Mauris on half of her papers, and a Schneider on half the others. She had so much trouble having a health care card, and a driver license and all her immigration papers because she had two different names. For the government, it’s been like if two different persons had been trying to do the same thing at once. And she said it herself, she should really have kept her real name, it would have been much less trouble. She had to go to the hospital once and showed her card, on which it was written Mauris (her husband’s name). The receptionnist took it to check into the systems and couldn’t find a Mauris. It happened she was in the system on her real name. It made such a mess because she had to pay for her visit into the hospital that day, since she wasn’t “registered”.
Getting back to the child’s name thing. Today, parents have the choice to either give the child his/her father’s or mother’s name, or even both of them. In all cases though, children usually end up using only one of their last names, the first one, and if they have children, they give them this first last name (getting confusing here… lol!) It’s like a priority order or something…