I launched the game, entered my name. I did not start the game. I saw customization, immediately went "oh, neat" and picked that option, which opened the browser, and there was the profile.
I do remember the johngaming had my nick after it with an asterisk (so it was something like "johngaming(*enonigmus)"). For clarity, I never entered any nickname as "johngaming", I only entered "Enonigmus" when prompted for a name to pick.
Also, I have now tried the game on a different computer. Also entered name as "Enonigmus". When I tried to open high scores/profile customization, I got an error from the site this time though. However, after actually doing a run, it did work and I could link the created "enonigmus-baldhairer" account to the other "enonigmus" account I had by renaming the account mentioned earlier. So, I guess this time it went normally according to what you described.
I guess if all the site tracks is a best score and some other achievements, then it's probably not a big deal I accidentally hijacked someone else's scores. It's just feels a bit dirty, and over all it's a bit odd. I don't mind my account being reset if it's required for fairness sake or whatever reason.