Type the first couple of letters in the username box: wait 15-seconds and the box will magically appear with usernames starting with that letter combination
If the username is still not there, type in another letter and wait. Usernames are case, punctuation, and space sensitive, so if a username is CamelCased, has punctuation, or has spaces, you will have to try those variations too.
If you have ever conversed with them, you could check the histories of your own talk page and talk page archives. Set your view to (500).
In your contributions, you could limit the namespace to user talk, and that would give you the names of all the users you have posted to on their talk pages. The same with the talk namespace (via your contributions).
You could also search the talk namespace for your own signature, to locate the threads where others may have replied to you
Where do they hang out? What are they renowned for? If you can remember where they have posted messages, then you can find their username.
Users Search box for users by name or official capacity
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