Deutsch is the
German word for 'German'. The words Deutsch and
Dutch are in origin the same word, as is
Teutonic and the Italian
tedesco (meaning 'German'), and also the first word in the Irish legendary
ethnonym the
Tuatha Dé Danann. It is the first part of the historical name
Theodoric, the modern German name
Dietrich, and
J.R.R. Tolkien's King
Théoden.
They all come from an Indo-European root teut- meaning 'people, nation'. This survived into Old English as théod, and the derived form théoden 'lord' used by Tolkien, but was mainly replaced by the word folc 'folk' (and later of course by the French borrowing 'people').
But as well as being Norse þjóða (i.e. thjódha) and Gothic þiuda (thiuda), it was borrowed into Latin as Teutoni, the name of a Germanic tribe in Jutland, later extended more widely to the Germanic peoples.
In the Old High German form diutisc it gave rise to the German word deutsch, the Dutch duits, and the English Dutch. Until quite recently "Dutch" referred to both German ("High Dutch") and what we now call just Dutch (formerly "Low Dutch"). In the name Pennsylvania Dutch it still refers to German. The German and Dutch languages, and the intermediate Plattdeutsch or Low German form a dialect continuum: there is no hard and fast boundary between them.
The Irish tuath 'people' is a separate development from the same Indo-European root.
King Theodoric the Ostrogoth was known in Middle German romances as Dietrich von Bern. They are the same name in origin. The French form is Thierry, the name of some early mediaeval rulers.
The -isc of the Old High German and the -esco of the Italian are the same suffix as English -ish and Scandinavian -sk, also used in language names.
It is possible that this root is also related to the Latin root tot- 'all', and to the Oscan touto 'city'. (Oscan is an extinct Italian language closely related to Latin.)