When connecting to a pluggable database, a valid service connection string that points to its service (previously configured and started) MUST always be provided, whether the connection is attempted locally or remotely:

$ sqlplus / as sysdba
SQL*Plus: Release 19.0.0.0.0 - Production on Fri Jul 30 17:32:15 2021
Version 19.3.0.0.0

Copyright (c) 1982, 2019, Oracle. All rights reserved.

Connected to:
Oracle Database 19c Enterprise Edition Release 19.0.0.0.0 - Production
Version 19.3.0.0.0

SQL> connect [USER]@[MY_PDB]
Enter password:
Connected.
SQL> show user
USER is "[USER]"
SQL> show con_name

CON_NAME
------------
[MY_PDB]
SQL> exit
Disconnected from Oracle Database 19c Enterprise Edition Release 19.0.0.0.0 - Production
Version 19.3.0.0.0
$ sqlplus [USER]@[MY_PDB]

SQL*Plus: Release 19.0.0.0.0 - Production on Fri Jul 30 17:31:24 2021
Version 19.3.0.0.0

Copyright (c) 1982, 2019, Oracle. All rights reserved.

Enter password:
Last Successful login time: Thu Jul 29 2021 17:35:38 -05:00

Connected to:
Oracle Database 19c Enterprise Edition Release 19.0.0.0.0 - Production
Version 19.3.0.0.0

SQL> show user
USER is "[USER]"

SQL> show con_name

CON_NAME
----------
[MY_PDB]
SQL>

Please do note that a service for the pluggable database ([MY_PDB], in this case) needs to exist, be running and serviced by the container database listener (which also requires to be running) in order for the connection to be successful.

How to create new PDB service

Steps for Creating a new Service for a PDB

Step 1. Change to pdb container;

sql> alter session set container=pdb1;

Step 2. Create service for current pdb using name and new network service name.

sql> exec dbms_service.create_service('pdb1','pdbprod1.example.com');

Step 3. Start the new service.

SQL> exec dbms_service.start_service('pdb1');
SQL> alter system register;

Step 4. Check the listener services and try to make a new connection to the newly created services.

Step 5. Save the state for PDB. Need to save the state for pluggable for the new pdb service. Otherwise, you need to manually start the service after you restart the pdb or bounce the CDB ROOT database.

SQL> alter pluggable database save state;