You can connect to a different database from within the psql prompt using below command where databasename is the name of the database that you would like to connect to.
\CONNECT databasename;
\c is the short for \connect . Below command can also be used to connect to a different database from within the psql prompt.
\C databasename;
You can also connect with a different role while switching between databases using below syntax:
\CONNECT databasename rolename; or \c databasename rolename;