The patient represented as "Irma" seems to have been Anna Hammerschlag, a widowed daughter of Freud's former Hebrew teacher, whom he was at this time treating for hysteria.

This from Jones's "Personal Life: 1880-1890" chapter:

Of the older generation Professor Hammerschlag, who had taught Freud the Scriptures and Hebrew in school, was the most important. Freud said of him,"He has been touchingly fond of me for years: there is such a secret sympathy between us that we can talk intimately together. He always regards me as his son." He had the highest opinion also of Hammerschlag's wife: "I do not know any better or more humane people, or so free from any ignoble motives." Years later Freud named his youngest daughter after a daughter of Hammerschlag's who in 1885 was married to Rudolf Lichtheim of Breslau, a man who died within a year; and another daughter after his niece, Sophie Schwab, whose wedding with Josef Paneth Freud attended.
(Jones, 1953, p. 163)

"Anna," perhaps more than coincidentally, was the pseudonym selected by Breuer for Bertha Pappenheim.