A key distinction between over-the-counter markets and centralized exchanges is the non-anonymity of the transactions. In this paper, we develop a model of non-anonymous trading and compare its prices, liquidity, and efficiency of asset allocations against a baseline with anonymous transactions. The non-anonymity improves the market liquidity by reducing the concerns for adverse selection. More specifically, it allows the market participants to learn valuable information about their counterparties through repeated interactions and consequently enables them to form trading relationships. However, it could harm the market liquidity by increasing the dealers' bargaining power, as the dealers learn more about their clients' liquidity needs. Our theory predicts that the bid-ask spread is smaller in non-anonymous markets, and more so for bonds with low credit-ratings, and at times of high uncertainty. The non-anonymity improves the allocative efficiency for assets with high volatility, with a higher degree of asymmetric information, and with less interest among liquidity traders. Using a novel dataset of U.S. corporate bond trades, we find confirming evidence that for high-yield bonds, the bid-ask spread for non-anonymous orders is 20% smaller than that for anonymous orders, while no such price improvement is observed for investment-grade bonds. By examining the waiting times and execution probabilities in our dataset, we present evidence that differentiates our channel from search-based theories.