It will not show your domain that connect to the social media, instead showing the developer domain which is weird and make it suspicious for customers.
We do have consent screen customisation and domain name can be changed. There're detailed instructions on how to do it available on the app page. And we're always here to help.
Open SignIn helps in login via different 3rd party login service providers (Facebook, Google, Twitter etc). Each of them actually requires an app, for example Facebook login requires Facebook app. When one installs Open SignIn all the apps are auto configured. But Open SignIn gives option to have customized app wherein a store owner can add his / her own app customizing it the way they want, like store name or store url etc.
It's easy to setup custom apps, for example one can get instructions to setup custom app at https://open-signin.okasconcepts.com/facebook for Facebook. We also do help in setting up custom app if the store owner needs help.
We would be happy to extend all possible help in this regard.
So, if you may please review this, it will be helpful for us.