We don't have it (BSD-3-clause + Patent), because nobody created it and submitted it to OSI for approval.
But theoretically, it can be created and it would be compatible with GPLv2, if the BSD+Patent license is also compatible with GPLv2. I don't see the BSD+Patent license in the GPL compatibility list, although it is presumably compatible with GPLv2, since the offending clauses in the Apache License 2.0 were the patent termination and indemnification clauses which are not present in the BSD+Patent license.
Anyway, the "endorsement" clause is considered to be not useful, for e.g. by the NetBSD project:
The members of the NetBSD Foundation (i.e. its developers) no longer
considered clause 4 (the "endorsement" clause) to be useful in today's
That said, the Apache License 2.0 is so much more explicit and detailed in its requirements, for e.g. with respect to trademarks. It is a much better license than BSD+Patent. It's also compatible with GPLv3, AGPLv3 and LGPLv3.
Even the GNU Foundation stated:
The patent termination provision is a good thing, which is why we
recommend the Apache 2.0 license for substantial programs over other
lax permissive licenses.
To add GPLv2 compatibility to Apache License 2.0, there are several better ways than dual-licensing it with the MIT license (MIT OR Apache-2.0):
- The LLVM Exception (Apache-2.0 WITH LLVM-exception).
- Dual-licensing the Apache License 2.0 with either the GPLv2 or LGPLv2.1.