Name of neurons affecting or being affected by a neuron?
At the simplest level, the terms 'pre-synaptic'/'post-synaptic' neurons should cover what you wish to describe.
'Afferent'/'efferent' are usually used to refer to axonal projections, usually between functionally distinct areas, or nerves. However, I wouldn't be too surprised if someone used these terms to refer to synaptically connected populations although I would consider it unusual. Simply, 'connected neurons' is also a term frequently used.



I will now go into a tangent to give you some background that should help you formulate an informed view about the vocabulary being used:

In areas that display a high degree of local connectivity, like the cerebral cortex and the hippocampus, any given neuron is connected with many different neurons. Hebb's theory of cell assemblies posits that a group of highly connected neurons may form over time in order to subsist a specific function. Given the high degree of connectivity, any given neuron will be able to participate in many different assemblies. It is often thought that these assemblies constitute the substrate of engrams, the physiological correlates of memory, at the level of the neuronal network. Hence, the concept of cell assemblies is prominent in our thinking about groups of synaptically connected neurons.

Setting aside the questions of the definition of the engram, recent efforts have claimed to identify engram cells under this or that experimental paradigm, although the connectivity of those cells has not been established. While we know that functionally similar neurons display a higher degree of connectivity and that groups of cells with correlated activity patterns can be formed by artifically-induced synchrony, the direct link between increased connectivity and behaviourally relevance has not been established.

On the other hand, only a handful of studies have directly measured the connectivity between more than two neurons (Song et al., Perin et al.), revealing the intricate properties of neuronal network structure. Depending on the level of description they may refer to distributed cell assemblies, synaptic clusters of neurons, $n$-vertex cliques, and motifs.

All this is to say that as soon as you start considering more than a pair of neurons, it makes little sense to talk about neurons that are exclusively connected with each other. As every neuron is connected to almost all other neurons in its immediate neighbourhood we often focus on the functional implications of their connectivity. Under this light, the concept of cell assemblies is central in modern neuroscience.