Cheryl has some explanation of the name of the group on her blog, and I thought I would add more here:

“The poor is a subjugated, exploited figure, but nonetheless a figure of production…the poor is distinguished by…its indispensible presence in the production of a commonwealth…the poor itself is power…the multitude is the common name of the poor…the poor, every poor person, the multitude of poor people, have eaten up and digested the multitude of proletarians…”
H&N, Empire, pp. 156-158

“The closer we look at the lives and activity of the poor, the more we see how enormously creative and powerful they are…the poor embody the ontological condition not only of resistance but also of productive life itself….All of the multitude is productive and all of it is poor.”
–H&N: Multitude, pp. 129-133