There is a party game where the players are allotted the name of some famous person, typically this name is written on a piece of paper and stuck to the players’ backs or foreheads so that everyone else can see the names except for the players themselves.
The object is that by asking questions that will take answers YES or NO that each player ascertains their “identity”.
What the hell is that called? Some have volunteered “Who Am I?” or “The Name Game”, but I remember this as being a Proper Name, Portsomething or other.
I believe the ‘Portsomething’ name you were thinking of may have been Portmanteau (or at least that is the name that was on the tip of my tongue when i read the OP) - Portmanteau is not the same game though; it is a game where novel words are invented.
Botticelli may be the name you were looking for, but I’ve always used that name for a different game, where the player comes up with the person to identify themselves. Others ask yes/no questions and the player answers.