Regarding the use of "Sol" in reference to our solar system, let's have a little fun and go through the process of reverse-Kryptonian linguistics, shall we?
I'll use my translation of the Kryptonian text from DSRW
as a template. Bear in mind this is
ALL HYPOTHETICAL, based on conjectures made from Kryptonian names (family, personal, and common nouns i.e. "H'Raka") as well as my own imaginative philological attempts at a reverse transliteration.
So, using the phrase
Hóxh vurk'tā síyktā edeag (my interpretation of the "You are not alone" text) coupled with
H'Raka, Kelex, Kelor, Dev-Em, Zor, Jor, Elsi, Dar-Enx, Syra Ten-Ar, Rao, etc., I can infer some patterns amid the apparent "chaos", and assuming that the Kryptonians did indeed know of human life on Earth and (presumably) intercepted one or both of the Voyager "golden phonographs", I can safely assume that their variant of "Sol" being phonologically similar wouldn't be out of the realm of possibility.
However, since I never assume that it isn't "that simple," and since Kryptonian is a language
far more ancient and homogenous than any human language, and for the sake of adding a little "flavor", let's assume that their approximation of "Sol" would be
Xhaó, with a pronunciation of "
K'shay-OH".
EDIT: I arrived at the final form
Xhaó, based on
Rao (which I assume will be pronounced "ROW" in the film)..I assume the
-ao phoneme as being the word "star"

t: