The name of my company is Fatfaces. Because is the singular form of the name I would make a possessive by adding 's at the end which sound very odd a. It would be - Fatfaces's customers. Is this right or should I just add the apostrophe without the s to fit the last noun of the company name which is in plural(faces)?
The possessive of singular nouns ending in -s are now standardized to the usual 's, with the sometime exception of classical and biblical names (Socrates', Jesus')-- though you will still find some varying opinions among style manuals.
This form of the possessive, however, is normally limited to nouns representing sentient beings-- a company would more often use the noun as an adjective: Toyota customers, Fatfaces customers.
In your case, howevver