Is there a name for what I'm describing? I suppose it could also be viewed as multiplying the amplitudes of matching frequencies from A and B. My goal is similar to a vocoder; I want to shape some synth-like wave to follow the frequencies of a vocal sample. Perhaps this is how vocoders already work, but I haven't seen any that allow you to provide your own modulation signal.
Exactly, that's how vocoder and convolution reverbs work.
What you are after is multiplication in the frequency domain, which is equivalent to convolution in time domain, and that's also how it is generally called: convolution. When the modulator is an impulse response you get a reverb, when it's something stranger a vocoder.
Good software to experiment with it are PureData and Reaktor. I don't know, but I bet there are VSTs that let you provide the modulation signal. Search for convolver and/or convolution.