[The actual sedes vacans, courtesy of Charles Cole].
At the time of writing, the Vatican website still has a separate page on the election of Pope Benedict XVI (if that link dies you can go here).
Annuntio vobis gaudium magnum; habemus Papam: Eminentissimum ac Reverendissimum Dominum, Dominum Josephum Sanctae Romanae Ecclesiae Cardinalem Ratzinger qui sibi nomen imposuit Benedictum XVI.
Now that is not what Jorge Cardinal Medina Estévez actually said.
Annuntio vobis gaudium magnum; habemus Papam: Eminentissimum ac Reverendissimum Dominum, Dominum Josephum Sanctae Romanae Ecclesiae Cardinalem Ratzinger qui sibi nomen imposuit Benedicti decimi sexti.
He clearly uses the genitive "Benedicti decimi sexti".
There are two things wrong with this. Firstly the Latin for "sixteenth" is sextus decimus not decimus sextus. If you search the Perseus database using Philologic you can use lemmas to show this. At Perseus under PhiloLogic put
The other thing wrong is indicated by the "official transcript". The Protodeacon should have used the accusative ending (-um) instead of the genitive (-i). The accusative is what was used in the past. It agrees with nomen, which is a neuter accusative (object of imposuit) and with which Benedictum is in apposition. When a noun is in apposition to another (typically a name as in "the orator Cicero", where Cicero is in apposition to orator) it agrees, so far as possible, in gender, case and number. Cicero, in his second speech against Verres, describes Syracuse in Sicily:
in hac insula extrema est fons aquae dulcis, cui nomen Arethusa est, incredibili magnitudine… (Ver. 2.4.118)
At the very end of this island is a fountain of sweet water, of which the name is Arethusa, incredible in size…
Arethusa agrees with nomen in case (nominative) and number (singular) . It does not agree in gender because there is no neuter form of Arethusa.
Camillo Cardinal Caccia Dominioni was Protodeacon at the conclave of 1939 when Pius XII was elected.
He clearly says "qui sibi nomen imposuit Pium". He also brings his hands together which strongly suggests (Italian stereotype) he has finished speaking and is not going on to say "duodecimum", although the video does immediately cut to a shot of the new Pope on the sedia gestatoria. It is somewhat nonsensical to mention the ordinal number. Papa Pacelli's name was not "Pius The Twelfth" but "Pius". The ordinal simply allows us to distinguish him from other popes of that name.
I cannot find footage of the relevant part of the announcement of John XXIII by Cardinal Canali in 1958. Here is Alfredo Cardinal Ottaviani announcing the election of Paul VI in 1963 (beginning at 2:40):
He says "…qui sibi nomen imposuit Paulum sextum". The numeral creeps in (the name "Paulus V Burghesius" of course was inscribed straight above his head on the facade of St Peter's [large jpeg]) but he preserves the accusative.
Pericle Cardinal Felici got to announce a new Pope twice. Here he is announcing the election of John Paul I on 26th August 1978 (from 0:55):
"…qui sibi nomen imposuit Ioannis Pauli primi". It is clear that he uses the genitive.
(You can add a wrinkle to the "John Paul I was murdered" conspiracy theory by noting that Cardinal Felici used an ordinal – "the First" – when there was no need, since no other Pope had ever had that name…unless he knew that there would soon be another. Note the uploader inadvertently suggests this is the announcement of Pope St John I (523-526). One of the commentators in this video of the announcement of the election of John Paul II (at 4:14) says that John Paul I chose to have the numeral inserted.)
Cardinal Felici was back on the evening of 16th October 1978 to announce the election of John Paul II. The fullest coverage is from this capture of the live broadcast by ABC News in the United States. Some journalists like to insert themselves into any story (the BBC coverage of the funeral of John Paul II was egregious in this regard) but these blokes just manage not to obscure what he says. The Cardinal gets to the name at about 2:05.
"…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.