What's the name of the problem of finding equilibrium concentrations?
I don't think the phrase "direct equilibrium problem" is used in this context.

"Multiple-equilibrium problem" would be appropriate.

As in the phrase "It involves solution of the multiple equilibrium problem" J. Molecular Biology vol. 247 page 774.

Or "chemical equilibrium problem" if you don't want to imply that there is more than one equilibrium.