Power Factor rating is a characteristic of load, Why Power factor rating is shown on generator (source) nameplate?

Normally, generators real and reactive power generation depends on the load according to the power balance equation. According to the load/demand power factor at the generators would be adjusted.

to inform at what PF u can get max Active Power.

Power Factor shown on Generator Name Plate is a Generator Manufacturer advise that how much Power Facor at Load side can be handled by the given generator without affecting its Normal Operation / Output Electrical Characteristics.

As Load side Power Factor further lowers in an Electrical System, Source Output in KW starts getting limited.