In the 1980s, I visited the Anne Frank House in Amsterdam. Newspaper clippings from the World War II era were posted on the walls. One clipping had the word "Duitschland" in a headline. I knew the Dutch word for "Germany" was "Duitsland" so this spelling puzzled me. My Dutch hosts explained it was an old-fashioned spelling for "Germany".
I gathered it was much like how English changed from "Tokio" and "Peking" to "Tokyo" and "Beijing" and also how the West is currently shifting to using the Ukrainian words for Ukraine cities instead of the Russian words. ( "Odesa" instead of "Odessa" and "Kyiv" insread of "Kiev")
Anyway perhaps this archaic Dutch word for Germany could have been used when the Dutch in the OP's TTL unified Germany. "Duitschland" is very close to "Deutschland", the German word for Germany.
The examples you give are all cases of less accurate transliterations of native names being replaced with more accurate ones. Except for Ukraine, there it's Russian based ones being replaced for Ukrainian based ones.
"Duitschland" in Dutch is a completely different linguistic change. It is plain and simply the original Dutch spelling, with "sch" being pronounced like the English "sh", as the pronunciation of the end or middle-"sch" in a shipload of words (Vlaemsch --> Vlaams, Nederlandsch --> Nederlands, but also visscher --> visser (fisher)) changed to "s", the "ch" part ended up being dropped.
FTR, in the 16th Century, and at least for some time into the 17th, "Duitsch" was actually used in the Netherlands to refer to both the language and its inhabitants (at least sometimes), with German-German being Hoogduitsch (High-German).
Similarities would've been much more apparent in the high middle ages though, and mainstream German ittl would anyway probably end up being low German, which is anyway a lot closer to Dutch. I think low German with a slightly Dutch flavour would end up the Lingua Franca of a HRE where a Flemish dynasty replaces the Hapsburgs and end up having Aachen as their capital. This probably requires France to have been clearly knocked out from the running, and the emperor is more clearly the suzerain of all Charlemagne's territories.
You might essentially end up with something like
Plattdüütsch or
Nedersaksisch. This is actually the twice the same language, the first being the dialect-in-Germany, the other the dialect-in-the-Netherlands, both clearly influenced by the local official language.