I call it mixme.tf which is not the actual domain of the website (yet, maybe, I dunno). However it is actually live under the URL https://mijuuu.github.io/ .
Basically you enter six names and press the 'mix me!™ ' - Button and it mixes your team randomly. I'm sure something like that exists already but if not feel free to do it better than me.
It is a work in progress and I am planning to integrate bootstrap to make it pretty and additional features like a copy box/button that copies the names and generated classes for you to paste into ingame chat or mumble chat or whatever.
Tell me how you like it and what you think I should add!
(Change on 26.10.2017)
I remade the entire thing with Material Design for Bootstrap. It looks pretty sick now imo, No functionality besides some links was added. Let me know what you think of the new look!
(Change on 27.10.2017)
I changed the website so that I can add more projects in the future. That means https://mijuuu.github.io/ will lead you to a welcome page from where you can click mixme on the top. Or you just go directly using https://mijuuu.github.io/mixme.html .
(Change on 2.11.2017)
I tried putting in some way to proof the mix. There is now a proof-button that screenshots the table and the copy box is finished. It's hard to fake the screenshot but you can still just hit mixme until you get what you want... If I made the mixme button only clickable once you could just refresh the page... I can't come up with anything else because github pages doesn't compile PHP or anything else dynamic which also means i can't get the steam API to work. Plus: Since this is a webpage you could always just change the HTML.
(Change on 3.01.2018)
I made it pretty on the phone so you don't have to minimize TF2 to mix your team :)
(Change on 29.01.2018)
I made mixme.tf for hl. I call it mixmehl.tf (creative, right?). You can find it under mijuuu.github.io/mixmehl. Not alot of effort went into it tbh. I copy pasted alot and didn't try and bugfix much. So it isn't the prettiest but it is functional.