Does Pseudomonas aeruginosa have any common name at all?
I think there's a difference between a vernacular or common name ("tiger", "cat", "pigeon", "elm", "pine") and a pet name or nickname as you use it here. The former are names in human languages for a particular kind of animal or plant, while the latter are a colloquial name used by professionals to refer to a particular species, often based on its scientific name.

I can't think of many micro-organisms that have a true vernacular name -- most micro-organisms were given fancy scientific names, and those were used consistently thereafter. The only proper microscopic common name I can think of is "slipper animalcules" -- but I'd be happy to be proved wrong! 

Lots of micro-organisms have pet-names -- E. coli, C. diff., "smallpox", "Ebola", "white nose", even Pelagibacter ubique -- but they're either based on the scientific name or on the disease the organisms cause. AFAIK (and based on the comments), Pseudomonas aeruginosa doesn't have one. However, of the list of species you list, only H. sapiens has a vernacular name, while the others only have nicknames based on their scientific name, so I'm not sure it's that surprising! IMO it's mostly macro-organisms that get vernacular names.