Relationships always see only the first related record. Your relationship should be based upon more than the last name - it should be based upon unique IDs and your User would select from a list. The list could be pop-up menu, portal, or filtered portal as your User types their name.
When you have a lot of people, it is best to create a calculation which concatenates something easily identifiable about a person, such as name and phone. This unique, easily identifyable reference is then used in your value list but NOT as the key fields. Each person record should have an auto-enter, FM-generated, non-modifyable serial number. Then your value list would be:
Use Values from Field. Select the ID in the left option and select the calculation in the right. Below specify all values and specify 'only display second values'. Attach this to your ID field (where people want to select) using a pop-up. Now people can select a person even if they have identical last name AND identical names at all. It is quite normal to have two Bill Smiths. This method will present the User with:
Bill Smith (206) 414-2479
Bill Smith (509) 222-2222
It depends upon whether you are selecting the person as you speak with them on the phone (so you can verify their phone number). Sometimes, using a street address works; sometimes the city. But I've had two Bill Smiths in same city as well. This would be a business decision on which fields to concatenate.
Concatenation is text calculation similar to: First Name & " " & LastName & " - " & PhoneNumber