As an Ashkenazi Jew, can I name my child after someone who is alive if they are not a relative or are you not supposed to name a child after the living, regardless of your relationship with them or their religion?
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There are certain circumstances where an Ashkenazi can name after a living person. They are discussed here. Most notably is naming after a living righteous individual or Torah scholar. That source also says if the person gives explicit permission, it would be allowed, but it doesn't source the claim (the author is a Rabbi, however) and that one was new to me, so I would encourage you to double check it.
As always, CYLOR.