From "A Practical Guide to Relational Database Design" from the year 2000.
"Each relationship line should carry a pair of descriptive elements, which define the nature of the association between entities. A name is a single word or descriptive phrase; it should always contain a verb such as: owns, owned by, holds, administered by, etc. Examples from our simple model are: A PART is sold on an ORDER LINE. An ORDER LINE is placed for a PART."
But, this has been lost because the practicality is that it is hard to know what is the element. As other comments points.
Probably the best is both worlds: PersonId_Owner. PersonId_Veterinary. Or something similar.
It seems that such a discussion should have been solved decades ago. And here we are. :)