Amazon sells Hershey bars through its site. I don’t think it needs to get permission to say “here’s the subscribe and save service to buy Hershey bars.”
I think the confusion is whether ElasticCo is endorsing or part of the service offering. So it should be clear that the offering isn’t by ElasticCo.
Back to the chocolate example, as long as Amazon doesn’t make it seem like Hershey is endorsing their site or offering the product they should be clear. I’ve seen this tucked into the fine print on stuff where it says that just because they are selling Hershey it has nothing to do with Hershey the company.
It seems odd that the company wouldn’t want it to be called AWS ElasticSearch as that’s what it is. ElasticSearch software sold as a service by AWS. Calling it something else is more confusing.