After you change vCenter name, the old one remains in vCloud Meter.

Problem with vCloud Meter is that this is not only reporting tool to VMware regarding your license usage (only for Cloud Providers). This is also your proof of compliance with the license agreement at any point in time.

For that reason, it is not recommended for you to do some changes inside vCloud Meter (os, shell, database) without support. 

Anyway, after you change vCenter name, there is no GUI option to do this respectively in vCloud Meter. Even if you remove vCenter, you are still unable to add it with the new name, as the UUID record is not deleted from the database.

One way is to change the proper entry in the database.

Please, make a backup (and snapshot) before you start with the procedure.

Procedure:

1.  select * from "VcServer";
2. search for the VC entry you want to change and write down the ‘id” entry.
3. execute the following: update "VcServer" set host = 'new_FQDN' where id = <id_value>; \q
4. service tomcat restart

Again, it is the best if you open the VMware support case so they can help you with that. Additionally, in the future there will be no issue to identify what happened with database and what has changed. Even if you struggle with this issue by yourself, it is worth to open case just to make it recorded.