If this question is dumb please excuse me.

Does this type of partition have a name and if so, what is it?

A sequence of partitions of an integer $\vec{\lambda}_1, \vec{\lambda}_2,....\vec{\lambda}_j $ such that the tuple of weights $(|\vec{\lambda}_1|,|\vec{\lambda}_2|,.... |\vec{\lambda}_j|)$ forms a partition of a fixed integer $n.$