Postpolymerization chemical modification ("coloring") of homopolymer brushes made of A units using B chemical moieties produces surface-anchored random copolymers (RCPs) A(1-x)B(x), where x is the degree of "coloring". We employ discontinuous molecular dynamics to study the "coloring" process in macromolecular tethers made of various lengths grafted at low and high densities on flat impenetrable surfaces. We demonstrate that the comonomer distribution in the A(1-x)B(x) RCPs depends on the interplay among (1) the length and the grafting density of the A-based homopolymer anchors, (2) the solubility of the parent homopolymer. and (3) the solubility of the B coloring units. Chemical modification of sparsely spaced chains on the surface leads to nearly random comonomer distribution in the RCPs regardless of the solubility of A and B. In contrast, the distribution of A and B units in RCPs prepared from homopolymers tethered at high grafting densities depends on the solubility of the parent homopolymer. Chemical modification of well-solvated A homopolymer grafts results in comonomer distributions that resemble those of diblock copolymers, comprising lightly modified blocks near the surface and heavily "colored" blocks at the top of the grafts. The relative lengths of the two blocks can be tuned by varying the solubility of B. Under poor solvent conditions, the distribution of A and B in the A(1-x)B(x), RCP is more complex: it is governed by the conformation of the parent A macromolecular anchors that form collapsed clusters before the coloring reaction.