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
To add this auto-randomizing template to your user page, use{{totd-random}}
Always good to peek into the future . . .
Tomorrow's featured article
Cucurbita (Latin for gourd) is a genus of vines in the gourd family, native to the Andes and Mesoamerica. Five species are grown worldwide, variously known as squash, pumpkin, or gourd depending on species, variety, and local parlance. The fruits have played a role in human culture for at least 2,000 years. First cultivated in the Americas before being brought to Europe by returning explorers, the plants remain an important food source. Most Cucurbita species are herbaceous vines that grow several meters in length and have tendrils, but bush cultivars of C. pepo and C. maxima have also been developed. Many North and Central American species are visited by honey bees, as well as specialist bees that pollinate only a single species. Most of the domesticated species can be considered winter squash, since the full-grown fruits can be stored for months. Their extracts have many uses, including in cosmetics. The fruits are also good sources of vitamins and minerals. (Full article...)