Hi In making possession nouns With old Greek name ,faustus, which one from the following is correct (faustus's bag / faustus' bag / faustus bag ) please answer it ,if we consider faustus is an old Greek name .

Actually, I would think that "Faustus" looks more like a Latin/Roman name, but that's not really too important here. Of your three choices, "Faustus bag," the one without any apostrophe at all, would definitely be incorrect for indicating possession by Faustus (but not necessarily always incorrect, e.g., if there were a line of bags known by the trade name "Faustus," then "Faustus bag" would be correct on the reading of "Faustus" as a proper noun functioning as an adjective premodifying the noun "bag").
Of your two remaining choices, with the apostrophe either preceding the possessive (a.k.a. genitive) inflection "s" ("Faustus's bag") or following the final "s" of "Faustus" ("Faustus' bag"), both ways are generally regarded as acceptable in Standard Written English. The choice really depends on how one pronounces the possessive form of "Faustus." After nouns ending in a sibilant like [s], many English speakers will chose to insert an unstressed vowel, sounding like "ih" or "uh," before the possessive inflection, thus changing the two-syllable "Faustus" into the three-syllable "fow-stuhs-sihz." If this is the pronunciation, then "Faustus's" is the preferred way to write this.
However, many other English speakers prefer not to add "s" to nouns ending in a sibilant at all to make the possessive (or plural) form, especially, as in the case of "Faustus," if such nouns are names (i.e., proper nouns). In this case, "Faustus' " would be the possessive form, and it would be pronounced identically to the singular "Faustus." However, other English speakers will still pronounce " Faustus' " as "fow-stuh-sihz," i.e., as though the possessive inflection were written as " 's "; there is considerable variation in actual usage.

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Menna Basha@MennaBasha1