Lots of other agencies/similar in other countries also use “ME/CFS” including the NIH and the CDC. So there is a precedent for agencies using two acronyms together in many contexts.
Yes, some agencies do use two acronyms hyphenated together on their website texts, for example.
In the case of NICE, using "CFS/ME" or "ME/CFS" isn't particularly problematic from a classification perspective, since NHS England uses the WHO's international edition of ICD-10 and CFS and BME (now ME for ICD-10 Version: 2019), are both coded to the G93.3 Concept Title code.
But the U.S.'s ICD-10-CM has BME coded to G93.3 and CFS (as CFS NOS) coded to R53.82, so these two terms are not aligned for coding in the U.S.'s ICD-10-CM, though the CDC does nevertheless use "ME/CFS" on its website texts.
But as I've said in my earlier post, CDC is responsible for managing and revising the content of the U.S.'s ICD-10-CM and is obliged to follow ICD conventions within the U.S.'s classification system for data collection.
ICD-10-CM codes are essential in the U.S. for billing and reimbursement. (For mental disorders, all categories in the DSM-5 are mapped to an ICD-10-CM code for billing and reimbursement.)
ICD-10 codes are also required by NHS England and there is a map between ICD-10 codes and the SNOMED CT UK Edition terminology system.
For example, if IAPT is successful in obtaining approval for its November 2019 request to add DSM-5's Somatic symptom disorder term to the UK SNOMED CT Edition, Somatic symptom disorder will be assigned a new SNOMED CT SCTID code. This new code will be mapped to an ICD-10 code for use in patient records and in the new IAPT Data Set v2.0 that is scheduled to be implemented on April 01, this year.