You can delete profiles at your myOsmo page (https://my.playosmo.com).

After you log in, click 'myProfiles' on top of the page, then select the profiles you wish to delete and click 'Delete'.

Please also see our PDF guide to myOsmo here:

https://www.playosmo.com/static/downloads/GettingStartedWithmyOsmoAccountsProfiles.pdf