Apple has significantly revamped the Contacts app in iOS 17. It added new features such as NameDrop, the ability to quickly and easily share contacts with others, without all that faff of having to send a text message or email.
You can add pronouns to your own contact card or other contacts quickly and easily as follows:
Tap on the Contacts app, and then from there tap My Card at the top to add your pronouns. Alternatively, to add pronouns to an existing contact, open up the details page for that contact.
From there, tap Edit and then tap AddPronouns. Select your language and add the correct pronouns.
You can also add pronouns in other languages by tapping Add Pronouns again.
To make the process as easy as possible, Apple also includes a primer on the correct usage of the three forms of pronouns.
Furthermore, when you use NameDrop to share your contact information, the default is to not share your pronoun information. Also, if you share another contact's information, their pronoun details are not passed on.
Along with iOS 17, this feature is also present in iPadOS 17 and WatchOS 10 and will be supported in MacOS Sonoma when that update is released later this month.