NDSolve supports matrix-valued dependent variables. So after removing the extra semicolon in the definition of H[t] we can do:

(*Commutator function*)
Comm[A_, B_] := A . B - B . A;

(*Define the master equation:dρ/dt=-i[H,ρ]-Γ/2[H,[H,ρ]]*)

eq := -I Comm[H[t], ρ[t]] - (Γ/2) Comm[H[t], 
     Comm[H[t], ρ[t]]] == ρ'[t]
(*Initial conditions from ρ(0)*)
initConds = ρ[0] == ρinitial;

Tmax = 10;
ρsol = NDSolveValue[{eq, initConds}, ρ, {t, 0, Tmax}]

i set n = 8 () for 3 qubits, still errors and no result.