While DWV is very standard term (the Home Depot near me uses it on a big sign near the pipe), novice plumbers probably do not know it. Once the tag is on a question I don't think the abbreviation is too confusing since there is a detailed tool tip that describes it in detail. However, many plumbing drainage questions get the "drain" tag but never get the DWV tag until it is edited by somone who knows about it.
I like the idea of actually spelling it out as I think it might help new people find the tag more easily. When they start adding a "drain" tag it will also show the new "drain-waste-vent" tag and they might actually choose it.
When I initially created the DWV tag is was to help differentiate questions related to "venting". I wanted to be able to tag plumbing vent questions with a different tag than the "vent" tag that people use for just regular air ventaliation questions.