With many names, especially female ones and names of countries ending in final -a, it is hardly knowable whether they have survived in English in their originally borrowed Latin forms or been replaced by later Italian ones unless the latter have taken different forms.
In the case of the name Maria, spoken English exhibits two versions: one descends from Latin and isn't given to the newborn nowadays but can be heard eg as the traditional pronunciation of the name of a Shakespearian character, in the no longer formally current expression Black Maria and so on. This spoken form rhymes with fire; the other spoken form rhymes with fear and is mainly heard as a foreign female name.
Numbers of popular English forenames have existed which are not necessarily derivable from French, German, Latin or Greek but are either directly borrowed from Italian or have been invented after Italian models including many of the following: Amelia, Andrea, Angela, Angelica, Anna, Annabella (apparently coined in Scotland), Antonia, Belinda, Cecilia (nowadays usually given an Italian-style value to its stressed vowel), Celia, Clotilda (cf Italian Clotilde), Cosmo, Davina, Jamesina, Gemma, Griselda, Jessica, Julia, Justina, Laura, Lauretta, Leonora, Loretta, Miranda, Louisa, Martina, Matilda, Nicola, Norma, Orlando, Perdita, Renata, Robina, Romola, Rosetta, Silvia, Sylvia, Teresa, Una, Vanessa, Venetia, Viola etc.
For expressions required to describe the geography of present-day Italy, English often uses terms descended from Latin or from earlier forms of Italian. These include the names of the seas surrounding the country, viz Adriatic (adriatico), Ionian (ionico), Ligurian (lìgure) and Tyrrhenian (tirrèno); and the names of natural features like the various Alpine regions Cottian (Alpi Còzie), Graian (Alpi Graie), Julian (Alpi Giulie), Maritime (Alpi Marittimi) and the Rhaetian Alps (Alpi Rètiche), the Alban Hills (Monti Albani), the Apennines (Appennino Centrale etc), the Dolomites (Dolomiti), and the Tiber (Tévere). Area terms include Apulia (Puglia), Latium (Lazio), Lombardy (Lombardía), Piedmont (Piemonte), Sardinia (Sardegna), Sicily (Sicilia), Tuscany (Toscana) and Venetia (Venèzia).
Among city names Leghorn has been replaced by the current Italian form Livorno, minimally Anglicised in pronunciation, to refer to the town. However, as a term for a kind of table fowl, Leghorn does seem to have survived to some extent, but not predominantly as suggested in the reference books, including even the Longman Pronunciation Dictionary, with stress on its latter syllable.
Regarding Milan, the Italian form (Milano) is now sometimes heard but mainly from speakers who don't mind being thought of as pretentious. Bradley in the Oxford English Dictionary in 1906 gave only the front-stressed pronunciation coinciding with the name Millan but Daniel Jones's 1917 EPD (English Pronouncing Dictionary) already classified that as a minority value and by 1956 the EPD labelled it as old-fashioned, no doubt none too soon, since the late stressing is now the only one heard in the UK and is also predominant in the USA except in reference to the towns there bearing that name. These have the even older initial vowel value as in mile. The word millinery is presumably very rarely identified today with the city of its origin.
Some city names have given rise to English-form corresponding adjectives including Neapolitan, Parmesan (fore-stressed in US but end-stressed in UK) Roman, Venetian.There are even English forms of some Italian personal names. These include Guelph (Guelfo), Ghibelline (Ghibellino), Petrarch (Petrarca), Raphael (Raffaèllo), Titian (Tiziano) and the saint Francis (Francesco).
The artist Michelangelo was apparently at one time quite commonly semi-anglicised to Michael Angelo and, although the spelling has been revised, the name is still probably mostly pronounced as if it were spelt in the former way.
In Shakespeare's day there were English forms of Machiavelli such as Machiavel but they're no longer used for the author of The Courtier.
The names of popes and kings of Italy are generally still Anglicised as a rule, eg Benedict for Benedetto, John Paul for Giovanni Paolo and Victor Emanuel for Vittorio Emanuèle and even sometimes Humbert for Umberto.Not only do English speakers have Italian names for Italian places but the great influence of the Venetian and Genoese empires in particular was responsible for the English use of essentially or chiefly Italian forms for many places whose home-language names are Arabic, Greek or Slavonic and either were never or are no longer Italian territories including many of the items in the following list: