"I don't think it is the right thing to do to use more than two user names on Stack Exchange."
That is really neither here nor there, since there is already ample discussion on Meta about multiple accounts with different user names.
If the accounts do not interact with each other, it's legitimate. In other words, if they are not used to upvote each other, or to circumvent bans, or to close or reopen questions, etc., then it's fine. Many users on SO have (for reasons best known to them) more than one username.
Some Meta responses may be pertinent here.
- People are allowed to have multiple accounts as long as they don't use them to vote for themselves. - Jeff Atwood
- Many people are very civil and will not engage in abusive acts when registering extra accounts. And for those that do, the rest of the community has proven to be very good at noticing these trends. - Grace Note
- It is not a problem to have multiple accounts, as long as they aren't voting for each other and doing other sockpuppet-y things.
- If you are not a moderator, you cannot know if a user is using multiple accounts, in the same way you cannot know if two accounts using the same display name are really used from the same person.
- If you found such false voting activity, just flag it for moderator attention with "other" option and write your description in text box. Moderator has better view and tool to find such users. You yourself can not perform such IP level activity, So better leave that matter with moderators.
- The chat is automatically associated with the account with the highest reputation.
- Users can always come back if their behavior improves. However, in this case, it is too much manual work to re-associate the deleted account, so the user should start at zero, or whatever the new accounts have. Probably better to start with a fresh slate anyway. - Jeff Atwood
- I think we should give people the benefit of doubt and assume that their intentions are honourable. ...perhaps keep an eye out for sock-puppetry but otherwise do nothing.
A user asking/answering with one account and downvoting with another... well, it's not against the rules, as long as one account doesn't interact with the other. In fact, it might be that the user doesn't want someone (maybe, like you?) keeping track of their down votes. Or are embarassed to DV. Who knows?
When in doubt, flag a mod. But please know that multiple accounts are sanctioned on SO.
Edited to add: I think all your questions are answered here, but to be on the safe side,
What is the procedure? Do we need to flag the question in need of moderator intervention and explain the situation?
As @Andrew Leach commented, if you think there is something shady going on (not just that there are multiple accounts), flag a mod and explain what you suspect with a reference to the unflagged action.
Is there any system to detect this kind of user on EL&U and ELL?
Yes, mods have the ability to detect such improper activity if they suspect it, look for it, or are pointed to it.
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