How are you these days?
As for your question, I think I had better paste OED's article about the etymology of Dutch than do any explanation.
Dutch, a., n. (adv.)
Also (4 duchyssche, 5 duysshe), 5–7 duch(e, 6 dou(t)che, dowche, duitch, dutche. [a. MDu. dutsch, duutsch, duutsc, ‘Hollandish, or, in a wider sense, Netherlandish, and even German’ (Verdam), in early mod.Du. duytsch, now duitsch, ‘German’, = Ger. deutsch, MHG. diutsch, ‘German’, OHG. diutisc, popular, vulgar.
OHG. diutisc, OS. thiudisc, OE. þéodisc, Goth. *þiudisks:—OTeut. *þeudisko-z, meant ‘popular, national’, f. OTeut. *þeudâ-, Goth. þiuda, ON. þjóð, OS. thioda, thiod, OE. þéod (ME. thede), OHG. diota, diot, people, nation. In Germany, the adj. was used (in the 9th c.) as a rendering of Latin vulgaris, to distinguish the ‘vulgar tongue’ from the Latin of the church and the learned; hence it gradually came to be the current denomination of the vernacular, applicable alike to any particular dialect, and generically to German as a whole. From the language, it was naturally extended to those who spoke it (cf. English), and thus grew to be an ethnic or national adjective; whence also, in the 12th or 13th c., arose the name of the country, Diutisklant, now Deutschland, = Germany. In the 15th and 16th c. ‘Dutch’ was used in England in the general sense in which we now use ‘German’, and in this sense it included the language and people of the Netherlands as part of the ‘Low Dutch’ or Low German domain. After the United Provinces became an independent state, using the ‘Nederduytsch’ or Low German of Holland as the national language, the term ‘Dutch’ was gradually restricted in England to the Netherlanders, as being the particular division of the ‘Dutch’ or Germans with whom the English came in contact in the 17th c.; while in Holland itself duitsch, and in Germany deutsch, are, in their ordinary use, restricted to the language and dialects of Germany and of adjacent regions, exclusive of the Netherlands and Friesland; though in a wider sense ‘deutsch’ includes these also, and may even be used as widely as ‘Germanic’ or ‘Teutonic’. Thus the English use of Dutch has diverged from the German and Netherlandish use since 1600.]
paco