One's best behavior, as in George never interrupts when we have guests; he has fine company manners. This term employs company in the sense of “guests.” An older variant, Tell me thy company and I'll tell thee thy manners, uses company in the sense of “companions.” The current term implies that one is more mindful of politeness with invited guests.
Examples from the Web for company manners
It had the opposite effect on her ladyship, who felt better after it; braced up again to company-manners after the first one.When Ghost Meets Ghost|William Frend De Morgan
It is the close of the movement, and company-manners will be wanted directly.Somehow Good|William de Morgan
These, be it understood, were company-manners, designed to impress.Kim|Rudyard Kipling