How do I change my name on Steam?

I have a name on Steam, but when I play multiplayer Team Fortress, it shows my email address.

I have already set my name in Steam, but I want the game to show my name.

Open your profile,

click edit profile,

change your name

and save the changes.

Note: Everything might not look the same, as I use some addins (steamdb is displayed in first picture, lastpass in third) and your language might be different.

Go to the Friends List, hit the arrow near your name, click "Change Profile Name", choose your Name, and you are done!

Thank you to ardaozkal for the image, Props to you!

If you want to change your username in the client (Note: You can still use my other answer in client), you can check @Magmagod's answer, or do this. This also works in games too, so you can change your name during a match etc.

Open up Steam Settings, then switch to the friends tab (if you are in-game, it'll automatically start from Friends tab):

Change your name, and hit the "OK" button.

Note: I'm using a theme, this might not look the same on your end.