Not many are reimplementations of existing, much more popular, already open source projects.

OpenSSH was a 'reaction' to the original SSH(.com) code getting closed source:

> OpenSSH originated in 1999 as a fork of Björn Grönvall's OSSH, which derived from Tatu Ylönen's original SSH 1.2.12 release, the last version distributed under a license permitting open-source redistribution before Ylönen's subsequent software became proprietary under SSH Communications Security.[4]

* https://en.wikipedia.org/wiki/OpenSSH

It was probably the second thing with the Open— prefix by this group of developers, OpenBSD itself being the first. They simply ran with the naming convention. OpenBGP/OSPF were developed as alternatives to Quagga (GPL).