Sorry to say that you can't customize the Service Desk notifications as you can in JIRA. For this we have the following suggestion where I'd advice you to set yourself as a watcher to receive new updates about this.
In additional and in case if you want to create different notifications, please check the Automation rules out as the following documentation:
Hello Community 👋, I'm a product manager at Atlassian, looking at improving change management capabilities across our products. In particular, we're looking at bridging the gap between Dev & ...
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