Hi. I need to figure out how to make a stick that has two specific NBT tags in Minecraft 1.15!

You have forgotten the escape sequences, you need forward slashes before and at the end of a string. Like this:

/give @p minecraft:stick{CanDestroy: ["minecraft:stone"],display:{Name:"{\"text\":\"Box Breaker\"}"}}

Or if you would not like the name to be italic:

/give @p minecraft:stick{CanDestroy: ["minecraft:stone"],display:{Name:"{\"text\":\"Box Breaker\",\"italic\":\"false\"}"}}