AWS Postgres DB "does not exist" when connecting with PG
I ran into this issue as well. It looks like the DB Instance Name and the actual DB name are two different things and even when you add a name when you create your DB, it defaults to 'postgres'. When I put in the name of my DB it gave me the same error. However, when I just put in 'postgres' it worked fine. Try that and see if it works for you.
The initial configuration of RDS instances is quite messy, since the parameter "database name" is only the name of the instance, not the proper name of the database. If you want AWS to create a database at the moment you create the db instance, you have to select "Additional configuration" and explicitly add a parameter called "Initial database name". Check the screenshot I attach here.