After decades of academic debate
over the use of the possessive form of eponyms in the naming of medical
conditions, the trend in journalistic style and scientific usage continues away from the possessive, toward the non-possessive form. However, in deference to the precedent set by
some longer-standing organizations (namely, the Bloom’s Syndrome Foundation,
the Bloom’s Syndrome Registry, and Bloom’s Connect), the Bloom’s Syndrome
Association has opted to err on the side of consistency. The BSA may readdress
this issue if public use of the non-possessive form enters the mainstream.
From Current use of medical eponyms – a need for global uniformity in scientific publications, Narayan J, et al. BMC Medical Research Methodology 9:18, 2009: "Conclusion: Inconsistency in the use of medical eponyms remains a major problem in literature search. Because of linguistic simplicity and technical advantages, the nonpossessive form should be used uniformly worldwide."
From the AMA: "…A major step toward preference for the nonpossessive form occurred when the National Down Syndrome Society advocated the use of Down syndrome, rather than Down’s syndrome, arguing that the syndrome does not actually belong to anyone.”