"…qui sibi nomen imposuit Ioannis Pauli." Again he uses the genitive but this time he leaves out the ordinal (conspiracy!).
I have the Ordo rituum conclavis (you never know when you will need to run a Papal election) which at n.74 at the beginning of chapter 5 has the following for the Cardinal Protodeacon to say:
Annúntio vobis gáudium magnum;
habémus Papam:
Eminentíssimum ac Reverendíssimum Dóminum,
Dóminum N …… ,
Sanctæ Románæ Ecclésiæ Cardinálem N …… ,
qui sibi nomen impósuit N. ……
So that is no help on the case to put the name in. The text at the Vatican website suggests that someone with enough power over the website at least, thinks that the accusative to agree with nomen is correct.
So far as I can tell the formula used three times since 1978 – nomen + genitive – means, apart from the obvious (So-and-so's name), "a reputation for" or "the word for". For obvious reasons (a search for any form of nomen returns 1251 answers from the Perseus database, for Cicero alone) it is practically impossible to dig out every example of nomen taking the genitive. Somewhere I made a note of the fact that in Cicero nomen amicitiae (genitive) means "the word for friendship". In the De Natura Deorum i.122 he has:
carum ipsum verbum est amoris, ex quo amicitiae nomen est ductum.
There is something attractive in the very sound of the word 'love,' from which the Latin term for friendship [amicitiae nomen] is derived. (Loeb [facsimile]).
In the De Finibus Bonorum et Malorum ii.78:
quid autem est amare, e quo nomen ductum amicitiae est, nisi velle bonis aliquem affici quam maximis, etiamsi ad se ex iis nihil redundet?
What is the meaning of 'to love' — from which our word for friendship (nomen…amicitiae) is derived — except to wish some one to receive the greatest possible benefits even though one gleans no advantage therefrom oneself? (Loeb).
And again in De Amicitia 92:
…delet enim veritatem, sine qua nomen amicitiae valere non potest.
…it utterly destroys sincerity, without which the word friendship (nomen amicitiae) can have no meaning. (Loeb).
On the other hand, there are examples of nomen plus genitive of X meaning "the name X" in passages when someone adopts a new name. Famously Octavian (the Caesar Augustus of Luke 2:1) took the name Imperator Caesar Divi Filius Augustus on 16th January 27 BC, an event which is taken as the start of the Imperial Rome. I don't have access to "Imperator Caesar: A Study in Nomenclature" by Ronald Syme which is the most important modern work on Augustus' name known to me. So far as I know the chief literary source for this event (Syme presumably also drew on inscriptions and coins) is Dio Cassius, a Roman who wrote in Greek. According to Wikipedia his Greek is full of Latinisms. Dio discusses the process in 53.16. Where necessary I quote the Greek and mention the grammatical form used.
And when Caesar had actually carried out his promises, the name Augustus [τὸ τοῦ Αὐγούστου ὄνομα – genitive] was at length bestowed upon him by the senate and by the people. For when they wished to call him by some distinctive title, and men were proposing one title and another and urging its selection, Caesar was exceedingly desirous of being called Romulus [Ῥωμύλος ὀνομασθῆναι – passive verb with a nominative], but when he perceived that this caused him to be suspected of desiring the kingship, he desisted from his efforts to obtain it, and took the title of "Augustus," [Αὔγουστος … ἐπεκλήθη – passive verb with a nominative] signifying that he was more than human; for all the most precious and sacred objects are termed augusta. (Loeb).
Suetonius mentions how the Emperor Caligula got his name in Caligula 9.
Caligulae cognomen castrensi ioco traxit, quia manipulario habitu inter milites educabatur.
He took the surname "Caligula" (genitive) from a joke in the camp, because he was brought up among the soldiers and dressed in a private soldier's uniform.
I would like to think that Cardinals Felici and Medina Estévez had been reading the primary sources for the renaming of Caesar Augustus – even though one normally takes Cicero's Latin as an example above the Latin of Suetonius or the Greek of Dio Cassius – but I think they were simply mistaken.
Jean-Louis Cardinal Tauran is the current Protodeacon. If he is elected Pope, presumably it will be the next deacon in precedence, Attilio Cardinal Nicer. Cardinal Tauran should use the form given on the Vatican website, putting the name in the accusative, and not in the genitive like his predecessors in 1978 and 2005.