After testing it out over the last month or so, Twitter has now confirmed that its new DM search option is being rolled out to all iOS users.
Get your search on. DM search is rolling out to everyone on iOS today.
— Twitter (@Twitter) October 1, 2019
The option, as you can see in the GIF example above, will enable you to search your DMs by name. That will then bring up any and all DMs from users with that name in their profile, including any group messages they've been included in.
The functionality is fairly limited, in that you can't search by message content - but then again, in combination with another Twitter DM search test currently underway, which would enable you to locate any content, including tweets, images and links, that's been shared within your direct message conversations, it could end up being fairly valuable.

That new option was spotted in testing last week, and if that gets rolled out, the two features would give you a lot more search functionality within your Twitter DMs, making it much easier to locate who said what, what they shared, etc.
Twitter has been making DMs more of a focus of late. All social platforms are seeing more activity shifting into private messaging, so it's no surprise to see Twitter also looking to cater to the broader messaging trend, but it is interesting to note how Twitter is looking to encourage DM use, and to consider what that might mean for your Twitter strategy.
Of course, Twitter's been trying to make more use of DMs for years. Back in 2016, Twitter tried to tag onto the then rising bot trend by emphasizing DM conversations for brand interactions.
Get faster and easier help from businesses. Try it now with @EvernoteHelps and @PizzaHut. #CarpeDM pic.twitter.com/T8vHnLESEM
— Twitter Marketing (@TwitterMktg) November 1, 2016
Those never really took off like Twitter would've hoped (which is actually in-line with broader bot usage in general), but with more conversations shifting to DM, and out of the public eye, there is still significant opportunity there, and Twitter's more recent DM updates show that it's becoming more of a focus.
These new additions are not specifically aimed at brands, but they definitely do have value from a brand usage perspective. Having the capacity to more easily sort through your DMs by customer name, or by content shared, will make it a much more appealing option for customer care.
The 'Shared Content' option hasn't been rolled out just yet, but it is worth keeping tabs on such developments, and considering where Twitter's messaging tools might fit into your broader platform strategy moving forward.