Wrong Italian translation

Even "resti imperiali" would be fine ; )

As soon as I typed "resto" on Google, the definition I received was "Parte residua di un tutto ( dammi il r. del dolce ; il r. dell'esercito si dette alla fuga ; dormì per tutto il r. della giornata ) ". If you notice, the second example is exactly about an army (esercito), which can fit the use of Resto in this particular case.
The same example (resto dell'esercito) is on Treccani site, which is for sure more reliable.

The very first dictionary that Accademia della Crusca suggests is Garzanti. Here, again, you can find "rimanenza, residuo", and this definition: "quello che resta di un tutto una volta che ne è stata sottratta una parte" (what remains of a whole once a part of it has been subtracted).

The meaning of "resto" you are referring to is another meaning of this word. Not the unique, not the most used one.

Little problem: I am Italian, and I know how to use a word in my language. In this context, they translated in a wrong way.
I can see that in English the affiliation is “Imperial remnant”, not “imperial rest”!. It’s the same difference.
The correct translation is one and only one: “reduce imperiale”.
Here the sense is “someone who still lives as imperial trooper once the empire is dead”. It’s a military context.
When we talk about people coming back from Wars we call them “reduci”.

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Is "reduce" the more fitting word in this context? Probably yes.
Is "resto" a wrong word? I don't think so...

Factions' names in SWGoH are given based on more than one criteria. Sometimes the faction name is related to the profession (e.g. Bounty Hunter) sometimes it's about the species (droids) and so on. In this case, it is a matter of affiliation.
So although the soldier who survived is called "reduce", the group to whom those survivor soldiers belong is the "resto".

This is how I understand it.

(I am also italian. Also sorry if my english lacks some grammar here and there!)