Giving players custom spawn eggs in 1.13
Solution 1:
I figured it out, I was trying to use {Tag:{ with no specifications. Using EntityTag was the needed change. This is the working command:
/give @p minecraft:shulker_spawn_egg{EntityTag:{CustomName:"\"Purple Turret\"",Team:PurpleTeam}}
From here it's possible to add subsection for the shulkers color, open height, etc... Thanks for the help!