The Elsfield branch is genuinely unnamed, according to the resident I asked who's been living there for 40 years. All the houses are named, not numbered. Causes them no end of problems with deliveries, apparently. I imagine so.

The only evidence to the contrary is one sewage pumping station by the roadside, but that probably reflects Thames Water's view of the world, and not ground truth.

I checked the riding stable and Montessori school's addresses online. No road names, just "Elsfield". Accordingly, I'm using addr:place=Elsfield for what I surveyed today, and not addr:street=*.
https://wiki.openstreetmap.org/wiki/Key:addr:place
(for where the streets have no name...)

The road does indeed point towards the now suburb of Oxford and former village, (Old) Marston. But there's not enough supporting address information visible *on the street itself* after an exhaustive survey. Ground truth trumps echoes on infrastructure labels!

Tagged as noname=yes on that spur.