15 cards where the text includes “choose” and the text includes “name” and the set type is core

Alhammarret, High Arbiter (Magic Origins #43)
Alpine Moon (Core Set 2019 #128)
Booby Trap (Ninth Edition #289)
Conundrum Sphinx (Magic 2011 #51)
Diviner's Lockbox (Core Set 2020 #225)
Infinite Obliteration (Magic Origins #103)
Necromentia (Core Set 2021 #116)
Phyrexian Revoker (Magic 2015 #225)
Pithing Needle (Magic 2010 #217)
Runed Halo (Core Set 2021 #32)
Shimian Specter (Magic 2013 #109)
Sorcerous Spyglass (Foundations #679)
Sphinx Ambassador (Magic 2010 #73)
Stain the Mind (Magic 2015 #117)
Vexing Arcanix (Eighth Edition #319)

This search is finished. Now the real work can begin.