With TypedPolynomials (as in your other question), the functionality @polyvar p[1:n, 1:n] doesn’t seem to be implemented yet.
However, it is is easy to construct the Variables matrix manually:
julia> subidx(i) = join(Char.(0x2080 .+ convert.(UInt16, digits(i)[end:-1:1])));
julia> n = 3;
julia> p = hcat([[Variable{Symbol("p", subidx(i), subidx(j))}() for i in 1:n] for j in 1:n]...)
3×3 Array{Variable,2}:
p₁₁ p₁₂ p₁₃
p₂₁ p₂₂ p₂₃
p₃₁ p₃₂ p₃₃