Change your name on Flickr
Looking for a new identity? Easily update the screen name that shows up on all of your photos and comments or your real name that shows up in your profile.
Change your screen name
Names already in use, even by deleted accounts, can't be used. Get creative and pick something unique!
Click your Buddy icon.
Click Settings.
Click Edit beside "Your screen name."
Enter your new screen name.
Click Save.
Change your profile name
Click your Buddy icon.
Click Settings.
Click Edit beside "Your profile."
Edit your info, then click Save It.
https://help.yahoo.com/kb/flickr-sln7309.html