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.
Simply put, a real name is worth more than a fake one.