in (one's) name
On behalf of someone or oneself. My late father was a huge animal lover, so I've opened up this animal rescue in his name. Since Mary wasn't home, I had to sign for the package in my own name.
in someone's name
1. in someone's ownership; as someone's property. The house is in my name. I own all of it. The car is in our names.
2. Go to in behalf of someone.