There’s a very simple business reason why Google cares if they have your real name. It means it’s possible to cross-relate your account with your buying behavior with their partners, who might be banks, retailers, supermarkets, hospitals, airlines. To connect with your use of cell phones that might be running their mobile operating system. To provide identity in a commerce-ready way. And to give them information about what you do on the Internet, without obfuscation of pseudonyms.
Follow the money.