What is the formal terminology for two species that are "close" to each other in a phylogenetic tree?
Are you looking for something like "sister lineage" (or "sister taxon" or "sister group")

This term may be more specific than what you're looking for, and to use it correctly you'd want to be a little careful – I guess in this case you might have to say something like: 


  "the lineage that includes chimpanzees and bonobos is sister to the
  lineage of which humans are the only extant species"


or


  "the lineage that includes chimpanzees and bonobos and the lineage of
  which humans are the only extant species are sister lineages"


both referring to this phylogeny.



It's also possible that explaining exactly what you mean by 'close', or what it entails, would be appropriate, be it Ilan's suggestion of % genetic similarity (or maybe genomic similarity?), # of nodes between your two taxa (again, this would have to be in reference to a specific phylogeny), or if you have a dated phylogeny you could refer to the time since divergence, as in "coding DNA divergencies ...place the most recent common ancestor of humans and chimpanzees at between 5 and 6 million years ago."(Wildman et al 2003).