It may depend on the server, but most shared servers prefix the database name to avoid duplicates. For example:
me _dolphin
you_dolphin
him_dolphin
You need to check phpmyadmin again and get the full database name, not just the dolphin bit.
The same applies to the user. It's usually prefixed as well to stop duplicates:
me _admin
you_admin
him_admin
When you fill out the page in your first screenshot, only enter the following:
Database Name:
Database User
Database Password.
It's not normal to get a 500 error at this stage. If the information is incorrect, you are usually redirected back to the page for another try.