> since, as you say, impossible for a Java implementation to be compatible without using the word Java in very many places, then this means that you are allowed to use that word without permission.

If this is true, then why did the Apache Harmony project have to close because it couldn't get a TCK license and so couldn't call itself Java or even Java-compatible?

Using the word "Java" in the human naming, branding, advertising material, etc is not required for technical interoperability and follows the usual trademark restrictions. Getting actual interoperability is protected, calling yourself compatible is a bit trickier.

Having a project branded "Magic Java Bean" with a class name com.mycompany.magicbean requires permission from Oracle, but having a project named "My alternative black magic drink SDK" with a classpath com.oracle.jdbc or java.something does not require any licence, if that particular name is required for interoperability.

TCK, despite "compatibility" in it's name, isn't required for compatibility in the legal sense (it's required to demonstrate compatibility, not as an unalienable part of any component that happens to be compatible) so it can be licenced (or not) however Sun/Oracle wishes.

Harmony didn’t shutter purely because they couldn’t license the TCK, but without a acceptable license to the TCK they can’t say they are a certified Java SE or Java EE platform. This meant they had no way to prove or verify compatibility, but they still continued to advertise themselves as an open source Java runtime environment.

Ultimately OpenJDK’s existence was what caused Harmony’s death, since the GPLv2 with Classpath Exception was a “good enough” license for the community (personal and commercial).