In both the case of Charging-Rule-Name and Charging-Rule-Base-Name rules are pre-configured in PGW
They are called as static rules.
In such cases PCRF just need to provide Charging-Rule-Name under Charging-Rule-Install AVP or Charging-Rule-Base-Name under Charging-Rule-Install AVP
Charging-Rule-Name is basically a single rule whereas Charging-Rule-Base-Name is a set of such rules.
While using static rule PCRF should be made aware of the rules present in the PGW.
This can be done manually while doing the policy.
For eg: In your case you want to install a Charging-Rule-Name of Charging-Rule-Base-Name during default bearer creation. In such case you can design a policy on PCRF that When APN Name received in CCR-I is lets say internet.apn and CCR-Type = 1(Initial) then you can send CCA with Charging-Rule-Name as X or Charging-Rule-Base-Name as Y which is already configured in PGW
If in any case rule name sent by PCRF is not present in PGW then PGW will send CCR-U to PCRF with PCC Rule Status AVP saying the status of rule as INACTIVE and and Failure-Code as UNKNOWN_RULE_NAME