What is the Maintenance DB asked by pgAdmin? pgAdmin dialog for adding new database connections asks for a "Maintenance DB".
In order to be able to connect, I set it to the database I want to connect (and also, I have the rights to connect).

So, why is it named "Maintenance DB" instead of "DB" or "Database"?.
It is worth mentioning that you are free to define any existing database in the cluster as "Maintenance DB". You are not limited to the options suggested by the interface, which are just typical defaults.

This is particularly useful for users with limited permissions or read-only access. Access to a single DB is simpler with the same DB as "Maintenance DB". Related:  


Do all users need access to the postgres database in pg_hba.conf?


What is the maintenance db? The manual:


  The postgres database is also created when a database cluster is
  initialized. This database is meant as a default database for users
  and applications to connect to. It is simply a copy of template1 and
  can be dropped and recreated if necessary.