This is pretty simple, but requires a bit of creativity :D You're naming a horse based on its parents' names!

Player One lists two names. Player two thinks up a creative name that incorporates both of Player One's names, then adds their own second name.

You can use animal names you've already used on HP, or real life horse names, or use a name generator! Just keep it HP appropriate ;D

Example play:
Player One: Devil's Ivy, Golden Girl
Player Two: Golden Ivy, Neverland
Player Three: Evergolden, Big Chex
Player Four: Golden Chex, Where's Dancer

I'll start off with Scarlet Science and Perfect Rascal

Devious Destiny, Giddyup Engo

Engo's Devious, Clumsy Majestic

Deviously Majestic, Always Never Yours

You're Always Never Majestic, Monsoon Season

Always A Majestic Monsoon, Mrs. Robinson's Caramel Thicket

Caramel Monsoon, Well Played 

Caramel Player, Wonderful Wonderful

Wonderful Caramel, The Lucky One

Lucky Caramel, Man of War

War of Carmel, Kissy Face

Warface Kiss, Mr. Brightside

Mr. Kiss, Enemy Lines

Mr Kiss Lines with the Enemy, Poolside Disaster

Enemy's Disaster, Sincerely Yours

Sincerely Disaster, Kiss Never Tell

Sincerely Disaster's Kiss, Loopin' Louey

Sincerely Loopy's Kiss, Allied Forces

Loopy's Forces, Jam-Bor-Whee

May the Force be With Whee, Lucky Charms

Force of Charms , Conspiracy Specified