What is an algorithm for making a net neutral molecule from a set of guessed positive charges? Given a set of partial charges for the atoms in a molecule, which are educated guesses but do not add up to zero, we would like to zero them in an intelligent way.

For example, if the net charge is negative and we see a +0.1 atom bonded to a -0.9 atom, we should probably shift the -0.9 towards zero to make that section of the molecule more neutral.

There is also chemical information which can be used, eg, keep oxygen atoms positive and don't let the charge on hydrogen be greater than 1.0. 

Is there a name for this class of problem? What algorithms can be applied?
Although you did not mentioned specifically, it is likely that you want to perform some Molecular mechanics force field calculations. The charges are important quantity, so you need more than educated guess to obtain usable results. Nonetheless, the problem of charge equilibration is solved by "Polarizable force fields".

It should be noted, that they are often more expensive, less reliable and less accurate than standard FFs.