The Latin root theodiscus is actually just the latinised form of the Old High German thiutisk from Indo-European teuta and means "people". Similarly, Alemanni means "all men". The Saxons were named after their typical sword or fighting knive, the Seax or Sax. It's still discussed where the term "German" originates from.

For good measure, in Arabic, Niemcy (actually “Namsa”) is what we call Austria. Germany is “Almania”, same as in French.

Of course, we have as many curveballs as you could want for European place names. Like Venice. Somehow we ended up with “Al Bunduqiya” for Venice. Have fun with that one.

Just to add one more sidenote: France is of course named after the Franks, a German people who lived next door to the Alemanni and the Saxons.

Any idea about how English came to call it Germany?

Niemcy and Nemetorszag both stem from old slavic “nem” (or something similar) meaning “mute”.

More precisely, the first one is from Proto-Slavic root *něm- ("mute") and suffix *-ьcь ("person with that characteristic"); ě was not quite the same sound as e, so linguists mark it with the haček, just as it is marked in Czech to this day. In modern languages the nationality is called: Ru. nemec, Pol. Niemiec, Cro. Nijemac... But the country itself is called Ru. Germanija (from Latin), Pol. Niemcy (literally plural "Germans"), Cro. Njemačka (actually a feminine adjective, taken from the syntagm "Njemačka zemlja" = "German land").

The Hungarian name is a combination of the Slavic loaned *němьcь > "német" ("German") and "ország" ("land"): Németország.

the “Alemanni” who lived in modern day Germany and bordered modern day france.

Alemans still live in Baden-Württemberg, parts of Bavaria, Switzerland and I think there's also a splattering in Austria. Basically, High Germans which aren't Austro-Bavarian (same culture, different kingdoms) are Alemans.

“Saksa” is derived from the German region “Saxony”.

That one can be a bit misleading: The modern state of Saxony has nothing to do with the Saxon tribe, the place the title was applied to slowly drifted over the ages. They're much more related to Prussians and Thuringians and even Franks, going all the way over to Flanders and Holland, than Saxons proper. (Holland, not Netherlands).

Here's a rough splotch of where Old Saxon was spoken, which you can consider "core Saxony". At least linguistics-wise it spread quite a bit especially during the days of the Hanse (becoming a minority language as far up as Estonia), but it definitely stops before arriving at a place where "goose meat" means "could you please". Utter gibberish.

I'm guessing saksa is more like the others and based on the Saxon people that once lived there rather than the modern region named for the same

thiutisk/ theodisk is from a Germanic/ old high German root meaning "belonging to the people"

As is the root of most self descriptions, the name of a group for themselves means "we" or "the people" or "humans".