There are laws about how people sign their names in a legal document. If it's good enough for that, it's certainly good enough for calling people to the Torah.
Rabbi J David Bleich has an mp3 on YUTorah in which two witnesses signed a ketubah; both were Russian Jews who signed their names as "ben Avraham." It turned out their fathers didn't have Jewish names, as far as they knew. Rabbi Bleich told them to transliterate whatever names their fathers had; thus, one was "Chaim ben Vladamir." (Though he insisted that "the old people in synagogue said I should be called up as Chaim ben Avraham!")
If the only [known] name is a non-Hebrew cognate of a Biblical name (e.g. the man was "Ibrahim" but never "Avraham"), Rabbi Yosef Eliyahu Henkin writes that the preference is to use the Hebrew/Biblical cognate, however it's also perfectly fine to simply transliterate the foreign cognate.
In short -- "ben Ibrahim" is definitely okay; "ben Avraham" would also be okay, unless there's a decent chance the father had some different Hebrew name. (I wouldn't worry about that one too much, honestly.)