The Japanese slang terms for the NES/SNES are "Famicom" and "Sufami" respectively. HAL Laboratories may not have felt that those terms would make for a good protagonist name, especially since the characters are supposed to be American with American sounding names (like Jeff and Paula). But "Ness" is an anagram of SNES and is similar enough to other English names like Jess, Jeff, etc. But it's important to note that in Earthbound, the name Ness is not so much the default name as it is the first of the suggested names if you "Don't Care" what the protagonist's name is. In the Japanese manual in fact, the Ness character's title is "Me" and in parenthesis it says "Nesu" and Jeff, Paula, and Poo are named Friends 1, 2, and 3. [1]

So even though NES might not have been a term known to the general Japanes public, it didn't need to be. Ness is not the intended name of the character, it is only the most common suggested name and hence more like an easter egg.

[1] https://motherforever.net/official-artwork-of-mother-2/