I believe you can't get a diagnosis of ME in the US, because the ICD code for CFS is always used, never the ICD code for ME.
I see a top specialist, who diagnosed me with ME/CFS, but uses ICD 10 code R53.82 for me and other patients, rather than G93.3, post-viral fatigue syndrome, which is supposedly the correct one.. But, many of us did not have a specific triggering viral event, so it's not appropriate.
It does allow investigations into causes of the fatigue, so that tests are usually paid for by health insurance. One notable exception is Aetna, who manages to exclude most of the tests and treatments I've found to be useful in uncovering treatable aspects of this disease:
http://www.aetna.com/cpb/medical/data/300_399/0369.html
This does present problems, as the policy for US Social Security Disability requires tests that are on Aetna's disallowed list.
As for US employer-based disability insurance, it is true most will cut a patient off after 24 months if the disability is mental health related. Part of the evidence they look for his weather patients have been prescribed psychiatric drugs. But, a diagnosis of R53.82 is not necessarily looked at as a mental health diagnosis.
However, if you look at the range of issues discussed on this site that various ME/CFS patients have, it becomes very clear that this is not a diagnosis of exclusion anymore, and that patients typically have a number of other ICD-10 codes, which are able to be submitted for disability purposes.
But, looking at the original question, most ME/CFS patients in the US refer to themselves as having ME/CFS, though there is no specific ICD-10 code that covers all of us. It's extremely uncommon for anyone here to say they have ME - this seems to be more of a geographic thing, with patients in the UK using that terminology, while some patients in the US may describe themselves as having CFS for short, with myalgic encephalomyelitis being strange and unpronounceable. More experienced patients, aware of the history, will usually refer to themselves as having ME/CFS. I've never heard a patient refer to themselves as having SEID, or a doctor here in the US giving that diagnosis.