Let's reframe this.

A person is living in an apartment building.

A person they dated is looking at an apartment.

Person 1 says Person 2 should mention their name so Person 1 can get the referral bonus.

Person 2 replies asking for a fair cut.

Person 1 refuses and offers an abstract reward instead.

The way I see it there are 3 problems.

1 - They "should" do something. "Should" means it is an opinion. Person 1 is of the opinion that Person 2 should help them get money without any clear benefit to Person 2.

2 - That Person 1 and Person 2 are of the opinion that even though they haven't actually done anything that they should each get the reward (or at least part of it).

Which means each one is looking at this in terms of their personal benefit instead of what is going to benefit then as a whole.

3 - The offer of an abstract reward is made in response to the request of 1/3.

Person 1 doesn't seem to have inquired as to why Person 2 would prefer the cash.

Person 2 doesn't seem to have inquired as to why Person 1 would prefer the abstract reward.

At best this is a case of poor communication, at best this is two people (one of whom claims to be dating the other) that failed to think about this in the context of them being a partnership.

ESH seems like the best option because both Person 1 and Person 2 appear to be looking at this incident in a vacuum rather than in context.