Does the name of the school REALLY matter? I noticed that no-name schools sometimes offer more concentrations than the well-known schools in online learning. When is it appropriate to choose the school (or cost) over a concentration?

This depends on your goals. For most people, the formal concentration means much less than the quality of the MBA.

It would really depend on which specific school.

In general a school's accreditation status - whether it's accredited by AMBA, EQUIS, or AACSB - is the first indicator of quality. After that it's a school's ranking, but as you note maybe some schools, even if they are not ranked, are good for certain placement fields.