What verb can I use for, for example when a real estate agent goes to a house and adds that real estate to his inventory with noting some specs, address etc.
What you are probably looking for is "to list [a house]". For example:
The real estate agent finished taking pictures yesterday, and is going to list my house tomorrow.
May not be quite what you're looking for, but you could say he is Cataloguing the house. The verb Catalogue both implies collecting information and that the item in question is one of many.
Interesting question. I'm not sure if "listing" is appropriate, since in your example he merely finalized an agreement or made a decision to try to sell it; "listing" it or "putting it on the market" seems like a later and separate act, requiring preparation and time. But I suppose that by "adding it to their inventory," a realtor/office could either be agreeing to the sale, or actually beginning to market it to the public
In your example about the realtor himself.....I'd say it's more a type of possession, though since the house does not belong to him in any sense, what he possesses is the "deal," or the right/opportunity to use it in business
In one sense he's claiming it (or the rights to its sale), though I think this word would only be used to emphasize a kind of personal victory over others attempting the same thing ("we all wanted a chance at the Andrews place, but Jim got there first and claimed it/snatched it up/grabbed it").
It might be better to say that he acquired the property. It has a similar 'possessive' meaning, but it is more neutral and less "grabby" sounding than claim. It's also used to describe the action of business entities, so would be very appropriate if saying that his firm "acqquired" the house/deal.
If we want to try something other than the possessive cluster, we could think of it as a job. "He talked to the owners and decided to take on the sale."
In legal papers, this act seems to be most often referred to as the agreement between seller and realtor, at which point he is designated as their agent in the matter.
I suppose these would all work, in certain contexts. I don't think there's a specialized term for the initial process and decision between the seller and realtor, like the term "listing" for when he tries to find a buyer.
Each and every area of specialisation (real estate, shipping, air freight) tends to have their own local special words or phrase to describe the aggregation of another item to the grouping.
It can be very frustrating trying to identify each of the special words, or worse, choosing a suitable well understood phrase for such packaging.
My personal example is of the software source control programme Git which can't agree (among many options) on the right word for the 'list' [index, staging area, manifest, cache, ...] of items being made ready.
Here in UK, houses are 'Listed' for sale by Estate Agents.
If it's retail, then I'd say to "stock" something.
To take note of. This may imply pen and paper depending on the context, but it can also just mean to make a mental note.