His holiness, the Pope himself, chooses his new name. There don’t appear to be any restrictions. The rules are set by the previous Pope.
Pope John Paul II, took the name of his predecessor Pope John Paul I, Albino Luciani, who was Pope for such a short time. John Paul I, took the names of John XXIII and Paul VI.
Someone else will have to confirm this, but
my recollection is that BOTH John Paul I and II saw their name as indicative of their mission, to continue the work of the Vatican Council, initiated by John XXIII and the teaching of respect for human life, which met such difficulty when Paul VI published Humanae Vitae.
There does seem to be another very practical consideration: the documents authored by the Pope are clearly distinguished from anything he produced before he was elected.
[JOHN PAUL II
UNIVERSI DOMINICI GREGIS
ON THE VACANCY
OF THE APOSTOLIC SEE
AND THE ELECTION
OF THE ROMAN PONTIFF](http://www.vatican.va/holy_father/john_paul_ii/apost_constitutions/documents/hf_jp-ii_apc_22021996_universi-dominici-gregis_en.html)
THE ACCEPTANCE AND PROCLAMATION OF THE NEW POPE AND THE BEGINNING OF HIS MINISTRY
87. When the election has canonically taken place, the junior Cardinal Deacon summons into the hall of election the Secretary of the College of Cardinals and the Master of Papal Liturgical Celebrations. The Cardinal Dean, or the Cardinal who is first in order and seniority, in the name of the whole College of electors, then asks the consent of the one elected in the following words: Do you accept your canonical election as Supreme Pontiff? And, as soon as he has received the consent, he asks him: By what name do you wish to be called? Then the Master of Papal Liturgical Celebrations, acting as notary and having as witnesses two Masters of Ceremonies, who are to be summoned at that moment, draws up a document certifying acceptance by the new Pope and the name taken by him.
- After his acceptance, the person elected, if he has already received episcopal ordination, is immediately Bishop of the Church of Rome, true Pope and Head of the College of Bishops. He thus acquires and can exercise full and supreme power over the universal Church.