They are written is special fonts, then copy/pasted into the username bar. They don't show up when you search for their user page (for example, "http://pokemondb.net/pokebase/user/fizz" doesn't show anything) if you use your regular computer font. However, if you copy/paste their name from somewhere on the DB ("http://pokemondb.net/pokebase/user/ƒιzz") it works.
Websites like this one allow you to experiment with funky fonts. For example, from that one site I can do:
Or you can use websites like this to flip text around:
You can also add keyboard symbols to your username, for example:
✓ ♥ ☮ ▲ → ← ♀ ♂ ✤ ♫ ★ ✦ ͡° ͜ʖ ͡°
I'm no expert on how the coding of this website works, so I don't know if it will accept some of the wackier fonts* or the upside-down one, but I'm 99% sure this is how these users get their funky names.
*Actually, if you go the the first link, the "Fraktur" font will not show up in this answer. So there are fonts that the website will not allow.