It appears that your package manager failed to create the database named $user for you. The reason that

psql -d template1

works for you is that template1 is a database created by postgres itself, and is present on all installations. You are apparently able to log in to template1, so you must have some rights assigned to you by the database. Try this at a shell prompt:

createdb

and then see if you can log in again with

psql -h localhost

This will simply create a database for your login user, which I think is what you are looking for. If createdb fails, then you don't have enough rights to make your own database, and you will have to figure out how to fix the homebrew package.

There are two different ways of creating a database in PostgreSQL. One is from the command line. The other is from the PostgreSQL console.

Command Line

In order to be able to create a database from the command line, you must first change to a user with rights to create a database. As you have shown with the \du command above, the user with those rights is postgres.

root@eric-desktop:/home/eric# su postgres
postgres@eric-desktop:/home/eric$ createdb prismatest2
postgres@eric-desktop:/home/eric$

As you can see, the creatdb command does not give any feedback. You need to confirm the creation by listing the current databases:

psql -U postgres -l
                                                 List of databases
    Name     |  Owner   | Encoding |   Collate   |    Ctype    | ICU Locale | Locale Provider |   Access privileges   

-------------+----------+----------+-------------+-------------+------------+-----------------+-----------------------

 postgres    | postgres | UTF8     | en_US.UTF-8 | en_US.UTF-8 |            | libc            | 

 prismatest  | postgres | UTF8     | en_US.UTF-8 | en_US.UTF-8 |            | libc            | 

 prismatest2 | postgres | UTF8     | en_US.UTF-8 | en_US.UTF-8 |            | libc            | 

PostgreSQL Console

Another possibility is to use the PostgreSQL console. To enter the console:

root@eric-desktop:/home/eric# sudo -u postgres psql psql (15.7 (Debian 15.7-0+deb12u1)) Type "help" for help.

postgres=# 
postgres=# CREATE DATABASE "prismatest3";
CREATE DATABASE
postgres=# 

To confirm the creation of the database, list the databases:

postgres=# \l

                                                 List of databases
    Name     |  Owner   | Encoding |   Collate   |    Ctype    | ICU Locale | Locale Provider |   Access privileges   

-------------+----------+----------+-------------+-------------+------------+-----------------+-----------------------

 postgres    | postgres | UTF8     | en_US.UTF-8 | en_US.UTF-8 |            | libc            | 

 prismatest  | postgres | UTF8     | en_US.UTF-8 | en_US.UTF-8 |            | libc            | 

 prismatest2 | postgres | UTF8     | en_US.UTF-8 | en_US.UTF-8 |            | libc            | 

 prismatest3 | postgres | UTF8     | en_US.UTF-8 | en_US.UTF-8 |            | libc            | 

psql assumes that you want to connect to a database, you can either provide one (just after the command) or it will assume you want to connect to a database whose name is the same as your username (or the account name of the process that started psql):

So, you could write:

psql my_db

or

psql -d my_db

or yet

psql --dbname=my_db

... and psql will connect to the (local) database named my_db.

You have more connection options that you can check in the documentation.

If you don't have yet a database created, check createdb.

In Database Navigator > Right click on PostgreSQL > Edit Connection

In Connection settings > general tab, enter your host (e.g. localhost), database (e.g. postgres) and leave User blank. Check Show all databases.

Right click on PostgreSQL and refresh. You should get a green checkmark in the PostgreSQL icon.

That's how I fixed mine, hopefully it'll work for you too.

Your database was created using double quotes so its name is now case-sensitive. Therefore, you now need to always use double quotes when referring to it:

drop database "Blog_test";

More details about quoted identifiers (a database name is an identifier just like a column or table name) can be found in the manual:
http://www.postgresql.org/docs/current/static/sql-syntax-lexical.html#SQL-SYNTAX-IDENTIFIERS

You need to double quote the name. In PostgreSQL we never double quote names. If you follow the convention, PostgreSQL will convert the unquoted identifier to lower case. In your case, that which created the db used double quotes.

Now you have a capital letter in the identifier.

From now on you have to double quote the identifier.

Not,

postgres=# DROP DATABASE RoutingApp_development;

But,

postgres=# DROP DATABASE "RoutingApp_development";