Webstore Customer Login Issue


Actually, I am getting an issue in "Customer Login" page.
My main 2 problems is mentioned below :

1) After customer login their details in the website, Can we show the "Customer Name" except to showing "My Account" as per highlighted in snapshot.

2) I have set up Google API for Customer Login but after click on "Allow" button again showing the login page for again login. What thing is remaining?

"Allow" Button shown in snapshot

I have set up correctly according to information but unable to find the exact issue. Kindly advise me what should need to be done to resolve the above issues.