Reserved by IANA on TCP; the UDP side belongs to 6a44, an experimental IPv6-behind-NAT44 mechanism.
IANA marks TCP 1027 simply "Reserved" — there is no service name and no assignee, so nothing is entitled to it. UDP 1027 is assigned to 6a44 (RFC 6751, Experimental), a scheme for giving hosts native ISP-prefixed IPv6 addresses from behind IPv4-only CPE by tunnelling IPv6 in UDP/IPv4; it saw essentially no deployment. Anything actually listening on TCP 1027 is therefore unregistered, and on pre-Vista Windows it is most often another dynamically allocated RPC endpoint from the old 1025-5000 range.
Expose with care
There is no standard service here, so you cannot reason about it from the port number — identify the owning process before deciding whether it should be reachable at all.
$ sudo lsof -nP -iTCP:1027 -sTCP:LISTENSeen this on your network? Beige Box scans your Wi-Fi and shows every open port on every device — and its Ports tool links straight back here.
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Corrections or a missing port? Reply @rimrocksystems.