"I have this code to show the users name:" is not showing any code.
a) Confirm you are logged into the portal, after signing in the contacts full name should be displayed in the top right corner (where originally it would have been signin).
b) if signed in, the Liquid {{ user.fullname }} should display the logged in users (contacts) full name if placed in an area that renders Liquid (e.g. the Page Content area) or user.firstname for the users first name etc (where the field name is the lowercase logical schema name of the column on the contact table including any prefix if any).
c) at a minimum the portal user will need a Web Role with a Table Permission on the Contact table of atleast 'self', Often this is already configured for the out of the box Authenticated Users web Role which is also by default set to be inherited by signed in users.
Generally you do not filter on text, the portal user is a Contact record and so to effectively filter you need your Tables records to be linked to the Contact (e.g. record has a Lookup to Contact that is populated with the user in question, or a many-to-many relationship), you can then either use Table Permissions to filter or Lists also can be configured to filter to the currently logged in user.
