This can be achieved using wix code. You need to create a custom login/register page in order to have your website name displayed when a user authenticates using google or facebook. To summarize what you would need to do:
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Place a HMTL iFrame on your page an enter the relevant HTML code into it to allow user authentication.
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Register your website on Google or Facebook to receive a client ID and Secret.
(once registered you can set the website address the user will see in the message during authentication) -
Add your client ID to the HTML iFrame code.
4 Add Javascript code to your page to receive the Google/Facebook user info from the HMTL iFrame.
5 Add Javascript code to your page to register the user on your website.
there is a useful link here to get you started https://www.wix.com/code/home/forum/community-discussion/solution-google-facebook-user-information-on-login