I'm not seeing a way to change the update posting in the property register.
Personally, I like to have
1. payee say Market Update
2. Category = _PropertyAssetUnrlzd (like what is done with stocks but for real estate)
3. Property tag = tag for the Property. (Property 1)
When I do property reports is nice to see the unrealized gain/loss of the property - which is just an estimate from zillow and usually wrong.
I can exclude this category or payee when running reports if I don't want to see it.