assign

decide as to where something belongs in a scheme

“The biologist assigned the mushroom to the proper class”

attribute or give

make undue claims to having

give an assignment to (a person) to a post, or assign a task to (a person)

select something or someone for a specific purpose

“The teacher assigned him to lead his classmates in the exercise”

give out

“We were assigned new uniforms”

attribute or credit to

transfer one's right to