Narayana's cows sequence satisfies the third-order linear recurrence relation N_n = N_n−1 + N_n−3 for n ≥ 3 with initial conditions N₀ = 0 and N₁ = N₂ = 1. In this paper, we study b-repdigits that are sums of two Narayana numbers. As an illustration, we explicitly determine these numbers for the bases 2 ≤ b ≤ 100. We also obtain results on the existence of Mersenne prime numbers, 10-repdigits, and numbers with distinct blocks of digits in the Narayana sequence. The proof of our main theorem uses lower bounds for linear forms in logarithms, and a version of the Baker-Davenport reduction method in diophantine approximation.