The prime suspect's name was Aaron Kosminski, not Nathan Kaminsky.
Two different guys, with Kaminsky (aka David Cohen) emerging as a more viable suspect, IMHO. From Wikipedia:
David Cohen (1865–1889). A Polish Jew whose incarceration at Colney Hatch asylum roughly coincided with the end of the murders. Described as violently antisocial, the poor East End local has been suggested as a suspect by author and Ripperologist Martin Fido in his book The Crimes, Detection and Death of Jack the Ripper (1987). Fido claims that the name 'David Cohen' was used at the time to refer to immigrant Jews who either could not be positively identified or whose names were too difficult for police to spell, in the same fashion that 'John Doe' is used today. This has been disputed by other authors. Fido speculated that Cohen's true identity was Nathan Kaminsky, a bootmaker living in Whitechapel who had been treated at one time for syphilis and who allegedly vanished at the same time that Cohen was admitted. Fido and others believe that police officials confused the name Kaminsky with Kosminski, resulting in the wrong man coming under suspicion (see Aaron Kosminski above). While at the asylum, Cohen exhibited violent, destructive tendencies that would today likely be linked to schizophrenia, and had to be restrained. He died at the asylum in October of 1889. Former FBI criminal profiler John Douglas, in his book The Cases That Haunt Us (2000), has asserted that behavioral clues gathered from the murders as well as linguistic hints from the "From Hell" letter (the only one he considers authentic) all point to Cohen, "or someone very much like him."Aaron Kosminski (1865–1919). A member of London's Jewish population, Aaron Kozminski was born in Klodawa Russia/Poland in 1865. He was transferred to a mental hospital in February 1891. He was named as a suspect in Chief Constable Melville Macnaghten's memoranda, which stated that there were strong reasons for suspecting him, that he "had a great hatred of women, with strong homicidal tendencies", and that he strongly resembled "the man seen by a City PC" near Mitre Square. (This is the only mention of any such sighting, and it has been suggested by some authors that Macnaghten really meant the City Police witness Joseph Lawende, though others suggest alternative explanations.). Written comments by former Assistant Commissioner Sir Robert Anderson and former Chief Inspector Donald Swanson claimed that the Ripper had been identified by the "only person who had a good view of the murderer" (a possible reference to witness Israel Schwartz, although many other possibilities have been suggested). However, they further stated that no prosecution was possible because the witness was not willing to offer testimony against a fellow Jew. In marginalia in his copy of the memoirs, Swanson said that this man was Kosminski, adding that he had been watched at his brother's home in Whitechapel by the City police, that he was taken to the asylum with his hands tied behind his back, and that he died shortly after. These last two details are quite untrue of Kosminski, who lived until 1919. His insanity took the form of auditory hallucinations, a paranoid fear of being fed by other people, and a refusal to wash or bathe. Kozminski also meets many of the criteria in the general profile of serial killers as outlined by John Douglas and Robert Ressler, including compulsive masturbation, unsteady employment, and absence of a biological father (his father died when Aaron was 8 years old). He also lived close to the sites of the murders. He was described as harmless in the asylum, although he had once brandished a chair at asylum attendants. He was previously reputed to have threatened his sister with a knife. These two incidents are the only known indications of violent behavior. The copy of Anderson's The Lighter Side Of My Official Life containing the handwritten notes by Swanson was donated to Scotland Yard's Crime Museum in 2006.
By the way, if you're ever in London, do the Jack the Ripper walking tour that Donald Rumbelow gives.