There are lots of German words that are reflexive, but we shouldn't necessarily translate them that way in English. You'd say "ich kümmer mich um den Jungen", but you wouldn't translate that to "I look myself after the boy" (while "I look after the boy myself" would require selbst or selber to be there in the German). "We do not surrender ourselves" isn't quite the same class of mistake, but it's still pretty awkward.
I'm thinking that because it is reflexive, "ourselves" is added. One could surrender something else as well, like, "We do not surrender [our whatever].". The German sentence includes an answer to the question "what do you surrender?". The English translation does not without adding "ourselves".
I'm not saying I'm right, I'm not a native speaker in either language. I'm guessing that's why "ourselves" is added here but, again, it depends more on context in the case of the English translation.
Please correct me if I'm wrong.
German is loaded with reflexives in a way that English is not. You can say We will not give ourselves up which carries the meaning of We will not surrender, but a natural English speaker will not tack on ourselves when using the word surrender.
It's true you can surrender an object or an abstract object, but without an explicit object surrender is talking about the subject.
Shouldn't "We will not surrender" also be considered correct? I think in German when you say "Wir ergeben uns nicht!" it also signifies the intention, not just the statement of fact, correct? (and in this specific case, and with an exclamation mark, I would actually think the context is saying this as a response to being asked to surrender, in which case "we will not (surrender)!" is even better of a translation, no?)
"sich ergeben" has primarily military connotations. "Ich ergebe mich." could be used to end a shooting. There is also: "Sie ergaben sich dem Feind." (They surrendered to the enemy.)
"übergeben" is used with an object: "Ich übergebe ihm die Schlüssel." ( I hand him the keys.) But careful: "Sich übergeben" means to throw up. "Er musste sich übergeben."
"aufgeben" has at least four different meanings: 1. "Er versucht das Rauchen aufzugeben." (He tries to quit smoking.) "Sie gibt das Tennis Spielen auf." 2. "Der Boxer hat aufgegeben." (The boxer has surrendered.) Also possible with chess players. 3. "Der Chef hat mir aufgegeben, die Maschine zu reparieren." (The boss has ordered me to fix the machine.) This sense is very common at school: "Hausaufgaben" is "homework". "Was hat euch der Lehrer aufgegeben?" "Was habt ihr auf bekommen?" short: "Was habt ihr auf?" 4.. "Ich habe das Paket bei der Post aufgegeben." ( I have posted the parcel.)