A N Other is a pseudonym for the person if you don't particularly know who the person is (such as when you are demonstrating where to sign a cheque) or if the person wishes to remain anonymous. In a way it is an anonymous pseudonym.
A N Other may be known as Anne Other if definitely female, Mr/Mrs Other, Mr/Mrs Average (in statistics), Mr & Mrs Smith (especially used in hotels), Mr/Mrs/Miss Blank.
As well as the above examples the person may be defined by what they own or where they spend most of the time such as: Mr Semi-detached, Mr Down the Mine etc. For past people we talk of Mr Smith (etc) of yesteryear, and the opposite is Mr Smith (etc) of the future.
If known only by a first name they are usually John if male, Jane if female. There is course Tom, Dick and Harry but they aren't applied to one person. Jonny is usually the name of a child (but also John and Jane).
More specialised versions would be Tommy Atkins (used in the First World War), Walter Plinge (formerly used on theatre programs).
John Doe and Jane Doe are other examples.
Couples may be known as Mr and Mrs Smith, Mr and Mrs Bloggs, Mr and Mrs 2.4 Children (from the number of children the average family is supposed to have and so on).
The street A N Other lives on may be Any Street, Any Road, Acacia Road or High Street. The most common name for a road however in Britain is Station Rd, which is not used.