Add to it that announcing one's AoD aloud is probably giving your enemy, or even your temporary allies, the perfect tool with which to bend you over the table and fuck you up the butt without warning?
Yeah, no, not something most quasi-sane Hollow breeds are going to openly talk about. To do so with another is either a sign that they're dangerously broken, have no fucks left to give and are near suicidal, or they genuinely bonded to and believe whoever they're telling is trustworthy enough not to use said information against them.
I can't speak for the collective- Neither Ira the character nor Boss the player have spent a lot of time interacting with other Arrancar players/characters. For myself though.....
I quasi agree with Garra's point of view that Aspects aren't a thing that everybody should just know about and understand, but then circumstances arise. In Ira's case, it's pretty goddamn obvious that he's got something going on. Something about being pissy about something being a natural state for him. Even at his calmest he's got a little bit of simmering resentment. And just looking around it would be immediately obvious that other people are capable of expressing emotion other than 'ALWAYS ANGRY ALL THE TIME'.
It's actually a thing he's vaguely interested in, and 'researches' (nothing he does investigatively could be considered professional or serious) it in his spare time. Why are so many of his fellow soul-eating abominations so goddamn chipper all the time?
And in his case, he actually has someone kind of like him (Atrum) he can actually make direct comparisons to and such. Which is why there is/going to be so many deliberate parallels between them.
To be fair though, Ira's about as unsubtle as you can possibly get.
Head of Public Safety Tsukimiya arrives in Hueco Mundo, intent on bringing justice to the criminals who have fled to the desert realm hoping to evade the long arm of the law. She finds what she is looking for in the throne room of Las Noches...
In an attempt to fill the vacuum left by the Queen and Primera's deaths, Segunda Espada Levi Grisha makes a play for the throne and gathers the Hollow-Breeds in order to stake his claim.
Meanwhile, a Shinigami assassin on an unsanctioned mission strikes at a hospital, aiming to rid the world of the Quincy queen's newborn children. Several Quincy rush to the queen's aid as Lieutenant Ogawa escalates the hostilites between mortals and Shinigami.