If you’d rather not show exactly which ship you’re on, you can turn off ship visibility in Settings. Other users will see a general region, like “the Caribbean” or “the Mediterranean,” instead of your ship’s name.
This applies everywhere your ship would normally appear: your profile, Discover, and match celebrations. It applies to everyone who isn’t you, with no exceptions for matches or higher tiers.
You can turn this back on at any time. Changing it takes effect the next time your profile is shown.