I wouldn't apply the extra "name=*" tag to the yard unless it's officially named as such. I would also consider expanding the "landuse=commercial" to the entire lot since it looks like they're storing other cars and trailers outside the yard.

Additionally, rather than "office=towing" I would probably use "service:vehicle:towing=yes" with "shop=car_repair".
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            Published using OSMCha: https://osmcha.org/changesets/174627260
            