Elasticsearch is a name of an open source project. Why is calling something "Amazon Elasticsearch Service" a trademark issue? It's not Amazon's fault they called their company after the name of an open source software (the OSS came first btw). Also, IMHO calling it "Amazon Elasticsearch Service" is fair since it represents exactly what it is. Would it better if they instead took the code, made some closed modifications and then released a service around it with a new name? My thought is no.
This isn't unusual, many other open source projects trademarked the name of their project. Google has some guidance on why a project might want to do this.
https://google.github.io/opencasebook/trademarks/#unmanaged-...
Here is a list of open source projects whose name is trademarked by Canonical.
No one is asking Amazon to share profits with Elastic. Many people do expect Amazon to honor trademarks of other companies. Many people expect Amazon not to package proprietary features as if they were free and open source.
Lucene is a library that makes it easier to provide indexing and searching of "stuff". It's not a commercial product with a sales and consulting team. I can't think of a more apples and oranges comparison.