The definition requires hierarchical
It is an inappropriate word to use for this system.
It also carries too much baggage from the internet. Control, ownership, google and so on
WHY do you want to use a word that does not mean what SAFE is doing here? Why not use real correct words, like “name”
To give an example of the silliness of Domains for a simple naming system
The country has a water domains for the supply of the country’s water and the government department rules over the various regional water commissions which rule over the water boards in each county.
Then we introduce a wonderful system where each house collects its own water and extracts all the water it needs from the atmosphere. Would you call that water domains or the water board or water commissions or water department. No of course you would not. Its just house water.
So why take a hierarchical domain control system and use it for calling a simple NAME system that has no hierarchical anything or no control systems build in
Just renew your thinking and do away with inappropriate words for calling this system, do not fall into the trap of trying to redefine wards that have definite definitions already. It will cause confusion at best and at worse people using it the wrong way and getting into trouble trying to work out why it does not work like domains, which translates into users getting al sorts of problems because the web page designers are using it wrong