This question might seem slightly odd, since I'm trying to find a single word for a person who 'has' something yet does not necessarily own it.
Someone who has a house for example would be called an owner. However, someone who has a conversation does not necessarily own said conversation, yet still has it.
This is different from similar questions about possession/ownership since most of those questions refer to material things, in which case if one was in possession of something (i.e. a house) which doesn't necessarily belong to them you could simply refer to them as the 'holder' of said thing. And although you could probably refer to someone as a 'conversation holder', it seems inappropriate given the context of what it means to hold something, which still implies possession of some sort.
I was dwelling on the possibility of a conversation haver, however that word does not exist as a noun derived from a verb in the way that: someone who holds would be a holder. (Someone who runs would be a runner, etc.) Why is it that the verb 'to have' cannot be translated in the same way into a noun?
Those two men conversing at the table are conversation _________.
Conversationalists? (this implies they must be good at or fond of conversing, which is not necessarily the case)
Simply 'talkers'? (talking and conversing are not the same thing though).
As I write this I notice that this might also have to do with our usage of the word conversation, for someone who has a thought is simply a thinker, and the same with most other verbs I can come up with.
I guess the term 'interlocutor' could work, however it still does not refer to the idea of having as possible noun...