No. The name only means it’s made by the OpenBSD team, nothing more. If they made their own Python port, it’d be called OpenPython, even though the original is FOSS.

> Is rsync going closed source? If not, how is that the same thing?

Not closed source, but with rsync 3.0 it changed its license to GPL3, which a lot of folks don't like: BSD/MIT licenses have zero limitations on use and distribution, GPL2 (rsync 1.x, 2.x) forces one to release code, GPL3 (rsync ≥3.x) adds further restrictions.

Some folks want to distribute code with as few restrictions as possible. Other folks have a great good/goal in mind (e.g., 'all software is open source') and so add 'local restrictions' to hopefully achieve greater non-restrictions.

OpenBSD didn’t get its name from NetBSD going closed source.