How can I rename the top level site URL website name in SharePoint server 2010?
moss10/my/personal/ PS /SitePages/Home.aspx
How to Change
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Additional care needs to be given for personal sites since there is a pointer to it in the User Profile. If you make a change, you will need to change the user profile as well. Typically I do not recommend changing the site's URL for a person, even when their name changes since this is auto-generated.
My/Personal/ sounds like the managed path. You can try to backup and restore the site to a new location. This article gives step by step instructions on how to backup and restore a site collection or subsite (export / import).