Customer login issues – Magento 2.3.6

I have a weird issue.

when customers logins to our websites they can log in but on the top, it still says “login” and “create account”. It also says “not you?” and a “Welcome message”.

There is no logout button, and sometimes when they add products to the cart and you want to check out they need to log in again.

Does anyone know what this issue can be?