It all depends on the audience. With doctors there are too many different factors so I won't go into the various situations.
With the general public, I usually hand them a copy of the Key Facts document from the Feb. 2015 IOM report (see
http://www.nationalacademies.org/hmd/~/media/Files/Report Files/2015/MECFS/MECFS_KeyFacts.pdf).
But I usually don't even mention the name of the illness when I hand them the info. Partly it's because my brain fog gets in the way of trying to speak clearly. And partly it's so they don't jump to conclusions.
So, at least when it comes to written info, I use the name ME/CFS. Note that the Key Facts document does mention the SEID proposed name. It also mentions the need to change the name CFS because of incorrect assumptions. I think that information is useful for someone who knows nothing about the illness.
I thought I'd add a sample interaction. This happens to me at least every couple weeks.
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Person in store, most often the cashier: "Hey, that's a cool gadget!" (pointing to my folding seat/cane)
Me: "Yeah, I need this due to my illness."
Person: "Oh yeah? What is it?"
Me, on a good day: "I have trouble standing, problems with my heart rate and blood pressure. Here's a flyer if you're interested."
Me, on an okay day: "It's complicated. Want a flyer?"
Me, on a bad day: "Uh... uh... Here's some info."
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They usually take a flyer, either due to curiosity or to be polite. Who knows whether they actually read it. But I always keep a few in my purse. You never know.