Most online communications rely on DNS to map domain names to their hosting IP address(es). Previous work has shown that DNS-based network interference is widespread due to the unencrypted and unauthenticated nature of the original DNS protocol. In addition to DNS, accessed domain names can also be monitored by on-path observers during the TLS handshake when the SNI extension is used. These lingering issues with exposed plaintext domain names have led to the development of a new generation of protocols that keep accessed domain names hidden. DNS-over-TLS (DoT) and DNS-over-HTTPS (DoH) hide the domain names of DNS queries, while Encrypted Server Name Indication (ESNI) encrypts the domain name in the SNI extension. We present DNEye, a measurement system built on top of a network of distributed vantage points, which we used to study the accessibility of DoT/DoH and ESNI, and to investigate whether these protocols are tampered with by network providers (e.g., for censorship). Moreover, we evaluate the efficacy of these protocols in circumventing network interference when accessing content blocked by traditional DNS manipulation. We find evidence of blocking efforts against domain name encryption technologies in several countries, including China, Russia, and Saudi Arabia. At the same time, we discover that domain name encryption can help with unblocking more than 55% and 95% of censored domains in China and other countries where DNS-based filtering is heavily employed.