If I were just looking at the tag's name, I would assume that dnd-basic referred to all three of the Basic D&D editions (Holmes, Moldvay, Mentzer), since they're collectively called that in the wider community.
If Holmes needs its own sibling tag to the other Basic editions, I think something like dnd-holmes or dnd-basic-holmes (a bit backwards but fits our tagging patterns) or holmes-basic-dnd) (more like what it's called, but bucks our tag pattern) or dnd-holmes-basic (our “dnd-” prefix with the common “Holmes Basic” it's called attached), would be more fitting.
And if Holmes' tag gets renamed, I think dnd-basic would need to be retired — none of the three Basic editions have a better claim to it than any of the other two, so it doesn't work as a synonym of any of them, and they're each juust different enough that a Basic D&D editions umbrella tag probably isn't useful either.
Update: I just did some digging through SEDE and it appears that dnd-basic only existed for a short while, and was only ever used on questions that were later determined to be more correctly tagged with dnd-bx. So there isn't an active precedent on the site for using dnd-basic to tag Holmes. (It also appears that the original incarnation of the tag — and its rejected use for labelling Moldvay Basic — was my fault!)
Contrary to that though, our [dungeons-and-dragons] tag wiki says does suggest to use dnd-basic for Holmes. That's based on our original meta about how to tag the D&D family in general. In that answer, dnd-basic is listed for Holmes in the proposed hierarchy, which explains where the tag wiki got the suggestion. However, it's followed with this bit of discussion:
dnd-basic was being used inconsistently and often redundantly with dnd-bx and no one was using the right Moldvay tag because it was bx-dnd instead of dnd-bx (I synonymed it). I propose that we either a) make dnd-basic just for Holmes or b) make it a collection of all three Basics, though I am unclear what purpose that would serve. or c) remove it in favor of the three specific tags.
It seems that we never ran into the practical question of how to tag a real Holmes question until now, so we never formally resolved which of (a), (b), or (c) to go with. In practice (as seen in the SEDE query), (c) is what happened to the tag, for lack of real Holmes questions or pan–Basic D&D questions to test out the other two options.
Since I find it likely that (b) would be confused and used as an umbrella tag instead of meaning Holmes, and (c) has worked well and agrees with the sense of the issue I had before I went digging, I still think dnd-holmes-basic or a variant is what we should use for Holmes, rather than resurrect dnd-basic for Holmes.