No, the policy is to use your google.com address, with some exceptions[1]. This confuses a lot of people, as things done for fun by one person on weekends (maybe not even official 20% time) are mixed in with official projects.
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Is this for patches that occur on your own time without company resources? Even in jurisdictions (like CA) where they can't enforce ownership over what you did?
I am neither a Googler nor a laywer, but I think yes and yes - if you don't care about copyright ownership and only licensing (which most of the time is fine - you usually only care if you either want to commercialize it later or you want to make sure either you have standing to sue infringers or Google doesn't), there's an easy process for open-sourcing something and letting Google retain ownership, and a much more involved process for confirming that Google doesn't own it. So it's easier to let Google claim copyright and not argue about whether they really have had ownership.
Some relevant links are https://opensource.google.com/docs/releasing/ for the personal-project-with-Google-copyright flow and https://opensource.google.com/docs/iarc/ for the personal-copyright flow.