As these pages print it.
Alfredo III° and Alfredo III
The third Alfredo is named on the splash and again on the history page, and the two forms are not the same string. One has a degree sign. One does not. The alt text on the history portrait uses terzo in lower case, while the visible caption uses the Roman numeral.
The English article page titles itself The real Alfredo, with a trailing space in the heading markup, and does not write III or III° in that heading.
The splash portrait
The large photograph on the splash is images/big_alfIII.jpg. The alt is Alfredo, l'imperatore delle fettuccine. The visible line under the image is Alfredo III°, in italics. The degree sign is part of that line. There is no full stop after the degree sign.
Above the photograph, the orange line reads IL VERO ALFREDO ALL'AUGUSTEO. IL VERO is marked as Italian. ALL'AUGUSTEO uses an apostrophe. The portrait sits under that line and beside the address table. The address note covers the table. The caption Alfredo III° is not inside the table.
The file name big_alfIII uses III without the degree sign. The page shows the degree sign only in the italic caption. The alt uses neither III nor III°. It uses the word imperatore, in the Italian phrase, with a comma after Alfredo.
A smaller fork image on the same page has the alt Forchette d' oro, with a space after the apostrophe. That alt is not a caption for the portrait. The note on the fork keeps the fork image with the Pickford and Fairbanks sentence.

Three portraits on the history page
The history sidebar shows three photographs in this order. The first file is images/ALFREDO-Primo.jpg. Its alt is Alfredo I. The caption under it is Alfredo I. Alt and caption match, including the Roman numeral without a degree sign.
The second file is images/ALFREDO-Secondo.jpg. Its alt is Alfredo secondo, with secondo in lower case. The caption under it is Alfredo II. The alt and the caption do not match: one spells the word, the other uses the numeral, and the alt does not capitalise secondo.
The third file is images/Alfredo-terzo.jpg. The file name capitalises Alfredo and leaves terzo in lower case. The alt is Alfredo terzo. The caption is Alfredo III. Again the alt spells terzo and the caption uses III. Neither the alt nor the caption uses the degree sign that the splash puts on III°.
The heading above the history text is Alfredo's history. It does not say Alfredo III. The page title is Il vero Alfredo all'Augusteo: l'Imperatore delle fettuccine, with Imperatore capitalised after the apostrophe. The note on the three Alfredos follows the sentences that name Di Lelio, Armando and Alfredo III in the body, not only these captions.
How the body names him
In the 1950 sentence, the history page ends one clause with his son Alfredo III. The numeral is inside a strong tag, and a full stop follows III. There is no degree sign. The sentence says he continues the tradition after Armando came away from the local in Via della Scrofa.
A later sentence says Alfredo III, in fact, inheriting the inspiration of his grandfather and father, has the merit of continued worthily the path traced by his predecessors. The grammar is the page's: of continued, not of continuing. The sentence says he takes the name of this historic restaurant in the world. It does not add III°.
The opening sentence names Alfredo Di Lelio, not Alfredo III. The birth sentence says their firstborn and then Alfred II, without the o, for the child born in 1908. That Alfred II is not the caption Alfredo II under the second portrait. The note on 1908 stays with Ines, the firstborn, and the missing o.
Armando is named as Alfredo II in the sentence about the restaurant in Via della Scrofa. The portrait caption Alfredo II does not repeat the name Armando. The page leaves the reader to put the caption and the sentence together, and it never writes Armando III or Alfredo III°.
The real Alfredo, without a numeral
index-eng.htm uses the heading The real Alfredo. In the file the heading is followed by a space before the closing tag. The quoted paragraph begins The Real Alfredo, with Real capitalised, at Piazza Augusto Imperatore 30. It does not write III or III°.
That paragraph calls the restaurant the historical roman restaurant, with roman in lower case, and says the fettuccine have been known since twenties. It names Mary Pickford and Douglas Fairbanks. It calls Alfredo the creative man. None of those phrases is a numeral.
The splash, by contrast, puts III° under the portrait and also says the fettuccine are mixed by the Magic Hands of Alfredo Himself. Himself is capitalised. The history page's third caption is simply Alfredo III. Three pages, three ways of pointing at the same name, and only the splash uses the degree sign.
The logo alt on the history header is not a person's name. The logo file is images/logo.jpg. The Italian-flag image beside the menu has the alt english, in lower case, and it links to index.htm. That alt is not Alfredo III either.
File names and captions side by side
The splash file big_alfIII.jpg and the history file Alfredo-terzo.jpg are different images. One is captioned Alfredo III°. The other is captioned Alfredo III and alt-tagged Alfredo terzo. The notes do not treat them as one filename.
ALFREDO-Primo.jpg and ALFREDO-Secondo.jpg capitalise the whole first word in the file name. Alfredo-terzo.jpg does not capitalise terzo. The alts follow the file more closely than the captions do: Alfredo I matches Primo's numeral, while secondo and terzo are words in the alts and numerals in the captions.
No caption on these pages adds a surname to Alfredo III. big_alfIII.jpg is the splash file. Alfredo-terzo.jpg is the history file. The degree sign belongs to the italic caption only. Di Lelio appears only in the first sentence of the history, attached to the boy who starts the restaurant, not to the italic III° on the splash. The note on the moustache quotes the history line that calls the later smile the symbol of Alfredo, still without III°.
Questions
Does the history caption use the degree sign?
No. The caption is Alfredo III. The degree sign is on the splash caption Alfredo III°. The history alt is Alfredo terzo.
Does the second portrait's alt say Alfredo II?
No. The alt is Alfredo secondo. The caption below the image is Alfredo II.
Does The real Alfredo include a numeral?
No. That heading and the paragraph under it on index-eng.htm do not write III or III°.