We can easily rename a pluggable database. Follow below steps.

Start the PDB with restrict mode

SQL> alter session set container=PROD_CL;

Session altered.

SQL> shutdown immediate;
Pluggable Database closed.
SQL> startup open restrict
Pluggable Database opened.

Rename the pdb

SQL> alter pluggable database PROD_CL rename global_name to PROD_MN;

Pluggable database altered.

SQL> show con_name;

CON_NAME
------------------------------
PROD_MN

Restart the PDB

SQL> shutdown immediate;
Pluggable Database closed.
SQL> startup
Pluggable Database opened.

SQL> conn sys/oracle@cdb1 as sysdba
Connected.
SQL> select name,open_mode from v$pdbs;

NAME			       OPEN_MODE
------------------------------ ----------
PDB$SEED		       READ ONLY
ORCL			       READ WRITE
PROD			       READ WRITE
PROD_MN 		       READ WRITE