Last time I checked, no, you couldn't.
You could instead call the offering "Eznzt Service for MySQL".
A long time ago I had an open source project to manage mysql replication topologies, and I called it mysql-ha. At some point, they reached out to me about the trademark infringement.
They were nice about it, I did not get a legal notice or anything, just a contact from a MySQL employee pointing me to their policy (as in my response to your example: I could have called it ha-for-mysql), and requesting that I changed the name to make it compliant. I ended up with a full rename (called it highbase) and they were kind enough to give me a one year free subscription to MySQL Enterprise as a token of appreciation for my change.
In way that I think is interesting regarding the AWS and Elastic situation, what MySQL's trademark policy intended was to avoid the situation in which a third party could be confused by a product or project name (mysql-ha in my case) as to believe that MySQL, the company, was behind the offering. So any use of the trademark that made it clear they were not involved (as in the "X for MySQL" vs. "MySQL X") was ok.
A long time ago I had an open source project to manage mysql replication topologies, and I called it mysql-ha. At some point, they reached out to me about the trademark infringement.
They were nice about it, I did not get a legal notice or anything, just a contact from a MySQL employee pointing me to their policy (as in my response to your example: I could have called it ha-for-mysql), and requesting that I changed the name to make it compliant. I ended up with a full rename (called it highbase) and they were kind enough to give me a one year free subscription to MySQL Enterprise as a token of appreciation for my change.
In way that I think is interesting regarding the AWS and Elastic situation, what MySQL's trademark policy intended was to avoid the situation in which a third party could be confused by a product or project name (mysql-ha in my case) as to believe that MySQL, the company, was behind the offering. So any use of the trademark that made it clear they were not involved (as in the "X for MySQL" vs. "MySQL X") was ok.