It could perfectly well be called "Agency" or "Service" (like the United Kingdom Accreditation Service UKAS, for example). But "Body" is what it calls itself, for what that's worth:

"The structure and operating principles of the National Accreditation Body [...]"
https://www.enac.es/web/english/structure

And this is the generic term used in EC Regulation 765/2008, in response to which ENAC was created:

"The establishment of a uniform national accreditation body should be without prejudice to the allocation of functions within Member States."
http://eur-lex.europa.eu/legal-content/EN/TXT/HTML/?uri=CELE...

So you might as well call it that as anything else.

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Note added at 23 mins (2015-10-21 15:54:26 GMT)
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Having just seen Phil's proposal, let me add that I was taking it for granted that the name would be given in Spanish and a translation in English added in parentheses (at least, that is normal practice), but I certainly would and do bother. People with foreign language skills are prone to underestimate how opaque those without such skills can find even quite simple names like this. I think it is a basic courtesy to the reader to provide a translation. If it is not needed, no harm is done.

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Note added at 37 mins (2015-10-21 16:09:17 GMT)
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The EA (European Accreditation) page leaves it in Spanish, though it gives English versions of most of the other national bodies. They seem to think people can cope with French, German, Spanish and Italian but nothing else. I don't think there's any official basis for that attitude (and the name of the Swiss body is given in English). As for the names, there are all sorts: Body, Agency, Board, Service... Quite honestly I don't think it matters very much which one you choose, if you're going to give an English equivalent.
http://www.european-accreditation.org/ea-members