@Mushroom
And they actually do. I can tell the difference between an HM3, an AO3 and an QM3. Now I was never in the Navy, but as a Marine I worked closely with them and got to know quite a few of their ranks and ratings (and what the badges inside the rank meant). And even why some wear red chevrons, and others wear gold chevrons.
That is stuff you only see in their dress uniforms. Or the "working" equivalent of the dress uniform, something you'd only see Navy personnel wearing when working in an ("white collar") office billet where they're being image conscious.
On ship(excepting the quarterdeck watches or ceremonial functions), or most of the "working" (blue-collar) shore-duty posts they're going be in either their utility uniform(or whatever they call the BDU equivalent they started using after I got out) or in coveralls.
The Utility uniform only had "the Crow and chevrons" on it(plus any applicable warfare pins), and came in one color, black. If you were a "french fry" you didn't wear anything on your sleeve. E-7 and above were stuck in khakis though, but even for them, you'd only see their anchors on their collar, no indication of rating unless they were wearing a name-badge and you were close enough to read it.
If they were in coveralls, you had rank insignia on the collars for E-4 and above, but the french-fries are out of luck once more, no insignia. But in a change of pace, IIRC, they could have red or gold chevrons on the coveralls--it's been a number of years so memory is fogging up a bit over time on that part. Remembering which uniform items used pins, which ones had patches sewn on, etc.
(edit: I think Laz will allow this outside link, as I'm not linking another story site:
https://www.usamm.com/products/navy-coverall-collar-insig-rank
Yup, the above is a site with a catalogue for the Navy rank insignia for the Navy Coveralls. Notice the rating symbol is absent.)
Ostensibly, part of that is to make sure that in the event of an abandoned ship or a captured ship, it provides some obscurity as to what roles certain people performed on the ship(obviously more challenging on a ship capture).. As they'd likely be in either coveralls or the working uniform which doesn't have rating insignia, only rank. Which is where "Name, Rank, and serial number" becomes fun for the sailors, as their rate is only associated with their rank, but not the rank itself.