Roster
Etymology
From roster in the sports sense (a team’s list of players). The dating usage extends the metaphor — dating several people is "keeping a roster," with talk of "cutting" someone or the "starting lineup"; no single coiner is documented.
noun · /ROS-ter/
The set of people someone is casually dating or keeping in rotation at the same time.
What it names
It names the deliberately maintained lineup of romantic options — nobody exclusive, several kept warm. It borrows a team-management frame for dating, with all the cool detachment that implies.
Example
He’s not looking for anything serious — he’s just managing a roster.
Related idea
Distinct from a situationship, which is one undefined relationship; a roster is several people held at once, by design.