Ss Thomas Plus et Ioannes Piscator

The Familia Sancti Hieronymi or Family of St Jerome is an organisation from Clearwater in Florida on the western side of the Florida peninsula. It is
…a canonical association dedicated to the advancement of the Latin heritage of the Catholic Church, as it is reflected in the Church’s liturgy, in its sacred music, in its devotional life, in its official documents, and in its propagation of the Faith.
To that end they have produced various resources for learning Latin, not just to read and understand but to think in and speak it.  Browsing over their site I came across the Latin text of the Apostolic Letter of John Paul II which made St Thomas More the patron of politicians.
quibus Sanctus Thomas Morus gubernatorum, politicorum virorum ac mulierum proclamatur patronus
I was surprised since it is not conventional to Latinise surnames. In the Graduale Romanum and Antiphonale Monasticum – as well as in the supplement for the Archdiocese of Birmingham printed at the back of my 1954 Breviary – it is the feast "S. Thomae More", "of St Thomas More". He is also "Thomas More" in the latest edition of the Roman Martyrology.

I did wonder if this might be excess enthusiasm on the part of the FSH but the copy of the decree on the Vatican website has the same text. At the bottom is a reference to the Acts of the Apostolic See, where such decrees are formally published. There on page 76 of AAS 93 [2001] [pdf] we find
quibus sanctus Thomas Moras Guberaatorum, politicorum Virorum ac Mulierum proclamatur Patronus
I assume the typos (Moras for Morus etc.) are due to errors in the optical character recognition and not to errors in the original.

Thomas More was beatified with John Fisher and several others by Pope Leo XIII on 29th December 1886.  The decree of the Sacred Congregation of Rites was published in Acta Sanctae Sedis (the predecessor of AAS), the Acts of the Holy See, ASS 19 [1886-87] [pdf] on page 347.
DECRETUM Westmonasterien. confirmationis cultus beatorum martyrum Ioannis Cardinalis Fisher, Thomae More et Sociorum in odium fidei ab anno 1535 ad 1583 in Anglia interemptorum.
I cannot construe the opening but the sense is "in confirmation of a decree made at Westminster of the cult of the blessed martyrs John Fisher, Thomas More and Companions slain from hatred of the faith between the years 1535 and 1583 in England". The point is that throughout the decree Thomas More's surname is not Latinised.

More and Fisher were canonised by Pope Pius XI on 9th May 1935. The entry for "More (B.) Thomas" in the index to AAS 27 [1935] [pdf] on page 551 is as follows:
de martyrio et causa martyrii, 86; consistorium secretum, 129; causae relatio, 133; consistorium publicum et causae peroratio, 141 ; decretum de tuto, 159; consistorium semipublicum, 201; in solemni canonizatione, 202; homilia B. P. de eodem, 204.
The first document is a decree by the Sacred Congregation of Rites. He is "Thomas More" throughout with his Christian name in the appropriate Latin declension. The next is a minute of a private consistory  of the College of Cardinals of 1st April 1935 including an allocution by the Pope. On page 30 he says
…rogemus de beatis martyribus Ioanne S. R. E. Card. Fishero Episcopo Boffensi, ac Thoma Moro Magno Angliae Cancellario sanctitudinis palma decorandis.
…we ask whether the blessed martyrs John Cardinal Fisher Bishop of Rochester, and Thomas More Lord Chancellor of England may be endowed with the palm of sanctity.
Note that the surnames of both men are declined as second declension Latin nouns. There follows, on page 141, the minute of a public consistory held on April 4th. In the Latin explanatory note they are "Fisher" and "More" but in the text of the speech by Monsignor Bacci, Secretary of Briefs to Princes (one of the Pope's Latinists), they are "Fisherus" and "Morus".

The decretum de tuto on page 159 is the equivalent for a canonisation of the decree on beatification from 1886 quoted above. In the title and in the text they are "Fisher" and "More".

The semipublic consistory of 9th May 1935 is the actual canonisation. Again, in the explanatory note at the top, they are "Fisher" and "More" and, again, in the Pope's speech of introduction, they are "Fisherus" and "Morus" declined appropriately.

The pattern so far is clear. In the more bureaucratic texts the surnames are kept in their English forms but in the more solemn papal pronouncements (Bacci is said to be speaking in the name of the Pope) they are Latinised. However the formula of canonisation is as follows.
Ad honorem Sanctae et individuae Trinitatis, ad exaltationem fidei catholicae et christianae Religionis augmentum, auctoritate Domini Nostri Iesu Christi, Beatorum Apostolorum Petri et Pauli ac Nostra; matura deliberatione praehabita et divina ope saepius implorata, ac de Venerabilium Fratrum Nostrorum S. R. E. Cardinalium, Patriarcharum, Archiepiscoporum et Episcoporum in Urbe existentium consilio, Beatum IOANNEM FISHER, S. R. Ecclesiae Cardinalem et Beatum THOMAM MORE, laicum, Sanctos esse decernimus et definimus, ac Sanctorum catalogo adscribimus; statuentes ab Ecclesia universali illorum memoriam quolibet anno, die eorum natali, nempe IOANNIS die vigesima secunda Iunii et THOMAE die sexta Iulii inter Sanctos Martyres pia devotione recoli debere. In nomine Patris et Filii et Spiritus Sancti.
To the honour of the Holy and indivisible Trinity, for the exaltation of the catholic faith and the growth of the christian Religion, by the authority of Our Lord Jesus Christ, of the Blessed Apostles Peter and Paul and of Ourselves; after mature deliberation and often imploring divine assistance, and by the advice of Our Venerable Brothers the Cardinals of the Holy Roman Church, Patriarchs, Archbishops and Bishops present in Rome, we determine and define that Blessed JOHN FISHER, Cardinal of the Holy Roman Church and Blessed THOMAS MORE, layman, are Saints and we insert them in the catalogue of the Saints; decreeing that their feast on their day of death every year – namely for JOHN on June 22nd and for THOMAS on July 6th – is to be celebrated with loving devotion by the universal Church. In the name of the Father and of the Son and of the Holy Spirit.
So in the most solemn of the documents their surnames are not Latinised but in the homily immediately following they are. (N.B. "dies natalis" in the Latin literally means "birthday" but it refers to the day of a saint's death). In the gardens of Allen Hall Seminary in Chelsea is a mulberry tree planted by a previous owner of the land. Thomas More did own the land on which the seminary now stands and the mulberry was supposedly planted by him because he was attracted by the Latin word for it, "morus". I guess Fisherus was used for consistency.