If talking about ESXi name resolution (not guest OS name resolution), if your DNS servers are on different network, just configure the default gateway on ESXi hosts and allow DNS traffic (TCP/UDP port 53) between ESXi hosts and DNS servers.
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If talking about ESXi name resolution (not guest OS name resolution), if your DNS servers are on different network, just configure the default gateway on ESXi hosts and allow DNS traffic (TCP/UDP port 53) between ESXi hosts and DNS servers.