Within the British isles there were different conventions for surnames, the two most common are patronymic and occupational.

Patronymic meaning, your surname indicates your linaege down your father's line: John-son(son of John), McGregor(son of Gregor), O'Grady(son of Grady).

Occupational means your surname is indicative of your vocation or profession. Potters pot, Masons were masons, Tailor/Taylor made and fixed clothes, it's a fairly simple system.

Smiths worked metal, but there are various kinds of specialized smiths because different metals have different properties and eccentricities that require different kinds of skill or expertise. Some are more delicate, some hardier, so someone who worked with fine gold wouldn't necessarily be skilled at working iron.

Extending from this, the various color surnames we see in English(White, Gold, Black, Green), are generally occupational surnames related to various types of smithing. Whitesmiths were silvertin-smiths, Greensmiths were copper smiths, blacksmiths worked iron. This extends beyond metals as well: Naismith and Arsmith/nail smith and arrow smith.

Many colors that are not traditional surnames were simply not colors associated with particular types of smithing, and thus never became popular occupational surnames.

Edit: As my own followup question, and one I regrettably don't have the answer to: I'm curious if anyone knows the etymology/history behind how those various colors became so concretely associated with those metals(and more specifically, smithing them) in the first place besides the obvious superficial connection.

‘Red’ also comes up in surnames, but usually as ‘Roth’ and variations. Roth/Rothe, Rottmann, Reitman, and Rothschild are all examples. This is usually attributed to ancestors who had red hair or ruddy cheeks.