Why is a user allowed to have different names on differents sites? It causes confusion and all…
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It is allowed because each site has a different account. It is up to the users, to decide if they want to use the same username in all the sites, use a different name in a specific site, or use a different name for each site.
I personally use a single name because it's easier to synchronize the account information in all the sites. If I used a different name, I should edit the profile singularly, or remember I want to use a specific username in a site.
As said by Oded, there should be any confusion about knowing the username I use in another site, as my profile shows the list of the accounts I have in other sites.