At least in Android, tapping someone's username (including yourself) will mention them in chat, and tapping on a ping will open a DM instead. I'm not a big fan of either option since there usually isn't a need to do either, and you might accidentally tap on them and have to erase it.
Instead, short-tapping someone's name or ping should open a menu that displays the user's roles and has options to view their profile, send them a message, add reactions, or mention them (so you can still mention them easily). This would also be more similar to Slack mobile, where tapping a username simply displays their profile information.
Long-pressing would remain the same as it is now, and display moderation actions such as banning, muting from voice chat, or changing roles.