I think the problems you describe have nothing to do with the Popover. It appears to be working as it was designed to work. Instead, there appears to be significant issues with the basic design of your database. I perceive that you are new to Filemaker and relational database design.
I have a database with two tables that are related by names (of persons).
That is not a good idea. Names are not unique, subject to change and vulnerable to data entry errors--especially given the idiosyncratic ways that people spell names. An ID number associated with the person's name is almost always a better choice for such a pair of match fields used in a relationship.
The main table is the one used for all the tabs and the fields. The related table has information about the names in the first table (phone number, etc).
That description doesn't sound like you actually need a related table. Usually, (there are many exceptions to this), if you link a record in one table to a record in another, there are multiple records in one table, linked to a single record in another. For example, a person can have several different phone numbers. You can then set up a phone number table and link multiple records in the phone number table to one number in the "people" table. Maybe that's what you have here, but that's not what it sounds like to me.
But all of this is secondary to this issue:
There are up to 10 fields that would show a different name (each field has a different Field Name)
You should only have one field for a person's name. To list multiple persons, you'd create multiple records and enter a different person's data into each record. This then sets up the basic design needed so that you can link other records to your main table by Person--though to do so with an ID number is better than using their name.
Thanks PhilModJunk. That gives me a lot of information on how to organize the tables. I appreciate it.