I'm using MyOpenID as OpenID provider and I forwarded *.openid.dobrogost.pl subdomains to myopenid.com (using DNS CNAME entry). This lets me use piotr.openid.dobrogost.pl as my OpenID because MyOpenID hosts my OpenID delegating page for me. Is it possible to do the same with Google?
As mentioned in the link given by Ranon:
Now it is possible delegate OpenID to your Google account (not Google Apps).
No, this is not using the demo OpenID provider using App Engine. This is your REAL Google account!
First you need to enable your Google Profiles. Try to view your profile and edit it, there should be an option to set your Profile URL. You have two choices there: either use your Gmail account name (without the @gmail.com part) as your profile id, or a random number assigned to you. It's up to you to decide which one to use. Either way, that id is your profile id below.
Now add the following HTML code to your delegating page:
<link rel="openid2.provider" href="https://www.google.com/accounts/o8/ud?source=profiles">
<link rel="openid2.local_id" href="https://profiles.google.com/[YOUR PROFILE ID]">
And it's done. Now try login SO with your custom url!