Clint : 

He was on a mission for shield, his targets were your parents. Fury didn't tell him they his targets had a child. When he finished killing the targets he was about to leave when he heard crying. He went to the room and saw that over the crib said Y/n L/n. He felt guilty for killing your parents so decided to take you in as his own. 

Natasha : 

Before she was sterilized she was forced to have a child with hydra's top agent. About 1 month after her child was born she escaped. She named the child y/n. Clint came to kill her but when he saw the child decided to recruit her instead. She said yes. 

Wanda and Vision : 

They had decided to adopt a child. When to my got to the orphanage they saw one baby's crib was away from the others. Wanda went over to it. She asked why the baby was separated. The lady told her the child had powers and was a freak. Wanda adopted the 2 month old without hesitation. Vision decided to rename the child y/n. Yes 

Pietro : 

He didn't know that he had knocked up his ex till 10 months after they broke up. He only knew cause she came to his house. She handed him the baby and said "here. Her name is y/n. I don't want her." Then she left. He said "well y/n we're gonna have a lot of fun."

Bruce : 

Tony had caused him to hulk out. He was walking around smashing stuff when he heard a giggle. He looked in the direction of the noise. He saw it was a baby. He picked her up and she giggled again. It was so cute he turned back into himself and said "I think I'll name you y/n. If hulk likes you than I guess we can keep you. Let's go home angel."

Thor : 

Tony had told him about an orphanages and Thor really wanted to go to one so they took him to one. When they got there he saw you and k we you were the baby for him. The lady said he could name her and that she was 1 month old. He decided to name her y/n.