The noun clause or noun phrase is "whoever is next on the list".
First of all, it is a clause. Every clause must contain a verb and a subject. Every sentence has at least one independent clause. The noun clause is a dependent ond, meaning that this sentence can not stand by its own.
Second, it has a conjunction: whoever, that join the noun clause to the independent one.
"Whoever is next on the list" is functioning as a prepositional Indirect Object.