Confirmed the historical part: originally Guerrero ended at roughly 37.74527714837956, -122.42212282388057, where the one-lane San Jose Ave meets what's now the four-lane divided road; as late as 1881 that was called "Old San Jose Road" (the regular "San Jose Road" was what's now Mission St, but was renamed sometime between 1878 and 1881) -- https://davidrumsey.oldmapsonline.org/maps/b83c9fb1-49f3-5735-9227-778a580647ca/view has an overlay view.

On the SF Assessor/Recorder map for block 6616 (the one west of San Jose/Guerrero between 28th and Valley), present-day lots 2-9 face this road segment.  In 1954, a revision eliminated lots 2A-9A, consistent with widening the road as part of building the connector to I-280 (built 1955).  According to the recorder, current lots 6616008 (658 San Jose) and 6616009 (660 and 662 San Jose) are the only lots along that road with San Jose Ave addresses; north of that point, lots 6616001-6616017 are 1600-1640 Guerrero St.  (source at https://sfplanninggis.org/blockbooks/AssessorBlock6616.pdf)

So if we went by street addresses, on the southbound (west) side the transition happens at 37.74497597571873, -122.42241116140848, while the northbound (east) side transitions at 37.745325562283845, -122.42218224371348.

This isn't a precise answer to where in an official sense the physical roadway changes its name.  The Assessor maps draw San Jose as far as the bend, but their intent is to show parcel boundaries, not precise road designations.