No IANA assignment and no established use; the honest answer is that nobody owns this port.
IANA lists 10626 as unassigned, and Nmap's nmap-services — which is built from real internet scan data — has it as unknown at a very low hit rate. No documented application, appliance, or backdoor defaults to it. If you found it on a scan, the source is a locally chosen port: an application config, a Docker -p mapping, or a service that increments off a base port and landed here.
Expose with care
Nothing about the number makes it safe or unsafe. The verdict belongs to whatever service you find bound to it.
$ nmap -Pn -sV -p 10626 TARGETSeen 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.