I haven't found a way. Right now the default is the name of our shopify URL, which is not the same as our live store URL.
If this feature doesn't exist, I feel like it should be implemented as I can't possible be the only one with this issue.
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Ah I needed to fill out that little line there with the site name. Okay thank you sir for assisting!
I have checked your store settings, and I see that you have already set your actual store URL to be used as the question replier (in green, the purple one is for when replying to reviews in the first screenshot attached):
And it is showing up correctly in the review widget, please see the second screenshot.
Changes usually take some minutes to reflect in the storefront.
Let us know if you need further assistance.