A pseudonym is a persistent nickname or other handle that can be validated to belong to only those who have access to some credential, i.e. a password. See nym for the generic concept.

not an anonym

It must be distincted from an anonym which is a signature that many people claim or may use without any single credential, e.g. "we, trolls", which is not associated with a credential.

not a body name

It also must be distincted from a body name which is the name assigned by law to a person's physical body and personal identity, i.e. the name on a passport. Though body names can change, at any given time a person has only one such name, and possibly also a body number, e.g. a US SSN or CA SIN identity number.

There is often a loose association between body names and pseudonyms, when one's personal initials or a common nickname or abbreviation are used, e.g. "heasto" for Hayley_Easto. Nonetheless "heasto" or "HCE" remain pseudonyms unless and until the user makes an unchallenged claim, i.e. at User:heasto to actually be the same person as Hayley_Easto and that user actually is the one who signs as _user_HCE.

With open politics in force, for minimum confusion, a standard such as User:Hayley_Easto must be enforced, and that account used whenever something must be _signed_HCE. That is the standard applied by the open politics web and is implemented on any mediawiki-based service where users use real names.

disposable nyms

Most pseudonyms are disposable and accordingly difficult to trust (in the sense of believing there is a body and belief system behind it). Many trolls use pseudonyms, which can be for a variety of purposes, possibly personal security or protection of content if sysop vandalism or IP blocks based on wiki witchhunts are common. On a troll-friendly wiki it is a wiki best practice to use a troll name so that it's quite obvious that the pseudonym is not one that is intended to last or for others to "form relationships with or through", i.e. it exists to raise some questions/issues, make a point, and then disappear.

Sometimes these are called sock puppets and there is extensive debate on them, e.g. at Wikipedia see http://en.wikipedia.org/wiki/Wikipedia:sock_puppet their rules for sock puppetry including some hilarious pictures of puppets. A main concern is to ensure that sock puppets do not vote or make a measure appear more popular among the membership than it is - however, since there is no mechanism to solicit new troll point of view under Wikimedia rule, sock puppets remain in use to raise hypothetical or statistically valid viewpoint from those factions who are absent: those in absolute poverty or who do not speak the language in which the discourse is being conducted.

persistent nyms

Persistent nyms across many services are hard to guarantee without an interwiki identity standard. Always be wary of these. In general if you cannot google someone's nym and find one and only one body name associated with that name in the recent past, there is a high chance you are not dealing with someone you think you are dealing with.

Extremely stupid mistakes are propagated in this fashion, e.g. the quite common claim that everyone choosing a troll name using Wikipedia is Craig Hubley. It's a fun sport for we, trolls, to create such an account with the word "troll" in the name, do some ordinary editing, and wait around to see how long it is before someone calls us "Craig" or "Craig Hubley". Great fun. Among other things it shows who is devoted most to stupidity.

are not credentials

Sometimes pseudonyms are taken as being actual credentials, which is the single most abusive use, e.g. names like "policy@greenparty.on.ca" or "fundraiser@greenparty.ca" or "socialcapital" all suggest some power or authority on a subject. Unless it is part of a formal role account and archive scheme, use of such names is unethical and must be stomped on quickly whether there is open politics in force. For any such name it should be very clear exactly how role handoff is accomplished and there must be guarantees (for the organization) that passwords and received email and other priveleges associated with the credential, are then passed on. See OP-recognized credential for issues in credentials that are relevant to open politics itself.

Without a credential scheme, such pseudonyms as "a_GPC_member" or "a_Canadian_citizen" might be tolerated with some means of validation or authentication. But these are ideally role accounts that exist only to anonymize a posting.

It has been suggested that in order to ensure the right to vanish and allow people to change their minds, over time an attribution on an edit or posting might degrade to credential, meaning, it carries a person's name until some expiry date, after which it is only possible to determine that a person of a certain credential said it.

This would parallel the secret ballot which encourages the public association of people with their views before elections but hides and guarantees hiding of their expressed opinion in the poll. See political privacy for a deeper discussion of this.

as services improve

As open politics services improve, there is less and less tolerance for pseudonyms because there are more protections for anonymous trolls and whistleblowers. Until these are in force, some tolerance of pseudonyms is going to be required, so, in general, it's far better to work to advance along the path of improved open politics argument and participatory culture than it is to waste time asking "who wrote what" over and over.