They are very likely informally termed tautonyms or as the Wikipedia page tells me, linguistically called reduplicants. There's a page full of people with reduplicated names including:
- José José
- Justo Justo
- Kelly Kelly
- Lisa Lisa
- Thomas T. Thomas
The term is not used solely for names with reduplicated first and last names, but also for other variants such as Jar Jar Binks or Richie Rich.
Some choices are available. 'Mononym' is given by Collins for a specific circumstance:
mononym (ˈmɒnəʊˌnɪm) n
a person who is famous enough to be known only by one name, usually the first name.
[Collins English Dictionary – Complete and Unabridged, 12th Edition 2014. S.v. "mononym." Retrieved March 16 2016 from http://www.thefreedictionary.com/mononym ]
That is, a famous person known by only one name is called a 'mononym' (according to Collins). This is somewhat far afield, but the circumstance is unusual enough that context and the prefix would probably be sufficient to convey the more general idea of a one-named person, famous or not.
Wiktionary provides another option:
Noun
uninym (plural uninyms)
A single name by which a person or thing is known.
Wiktionary also supplies a source for the neologism:
1985, Jeff Millar, "Ups in engrossing Dragon' overshadow the downs", Houston Chronicle, 19 August 1985: Casting the role with the "uninym-ed" Ariane, a model taking her first shot at acting, is not what you'd call damage control.
(op. cit.)
Four other citations exemplifying use of 'uninym' in the popular press are given, from 2003, 2004, 2006, and 2009.
Of the two, 'mononym' and 'uninym', I would prefer the neologism 'uninym' over the neologistic use of 'mononym', which last has a history in the 19th century defined as "Chiefly Med. Obs. A technical name consisting of one word only" (OED Online). As noted, 'mononym' is obsolete in that sense. 'Uninym' appears to have greater contemporary currency.
Other options include 'monomial' and 'mononomial'. Both are used as nouns and adjectives. Although not obsolete, these virtually equivalent terms have very specific uses historically:
A. n.
1. Math. An algebraic expression consisting of one term only. Cf. mononomial n.
....
2. Chiefly Taxon. A taxonomic or technical name consisting of one word only; = mononym n.
["monomial, n. and adj.". OED Online. March 2016. Oxford University Press. http://www.oed.com/view/Entry/121489 (accessed March 16, 2016).]
The adjectival senses of 'monomial' and 'mononomial' correlate with the nouns. Attestations are given from the 19th and 20th centuries.
Best Answer
A hundred years ago, even in the US, men used last-name-only in addressing:
They added the title in addressing:
One addressed by the first-name-only
Women followed the same rules, with the sexes reversed, except that they addressed women equals by last-name-only only in (then rare) professional or school contexts, and the first-name "intimacy/familiarity" line seems to have been drawn a bit less stringently.
In the US, over the course of the last century, almost all uses have been swallowed up by first-name-only, except where tradition or professional discipline enforces use of titles to eminent superiors. I believe the same is coming-to-be in Great Britain, too; but you must consult a native speaker on that.
The use at Hogwarts in the Potter books reflects very traditional public-school practice, which spiceyokooko addresses in more detail in the Comments.
EDIT:
I am moved to add, in light of the discussion in the comments, that it would be gravely discourteous (not to mention deleterious to discipline) to omit a deserved title when addressing anyone in the presence of his or her subordinates.