You can place the related field (e.g. Team::LastName) on the layout of ProjectTeam. Make it non-enterable so they cannot modify it acidentally. If you prefer, you can place it over the ID selection field.
Another option is to use a popup menu insted of drop-down, with the value list showing only second field - but this requires the names to be unique.
I did as you said and hid the actual selection field (Team::_kp__TeamID) behind a calculated, non modifyable field (Team::Z_TeamNameFull). If i set the background color right the underlaying field is completely hidden.
When clicked upon a dropdown shows with values from the "Z_TeamNameFull" but actually the TeamID is stored.
_kp_TeamID = Primary identification key of the Team table, unique value. i.e. "105"
Z_TeamNameFull = Calculation field; (First name + last name) i.e. "John Andersson"
Thank you comment!
The solution was not actually what i thought it would be but the result is very much what i was looking for.