We'd have to decide if we are really committed to USD or not. In the past there was some discussion that the charter is really stable value and if USD deteriorated sufficiently we could switch to something else like a basket of commodities (I'd argue it should still programmatically inflate modestly, say 2%/y). In that case putting too much 'USD' in the name wouldn't make sense.
But on the other hand we could fully commit to USD and if USD really went bad we could create another coin (significant/infeasible development effort to do today at base level, but maybe someday).
On the other hand, I guess if the target changed the name could change again too.
I feel uneasy about making too many or too large steps at once but I think modestly altering the name could be a small first step - just to re-orient people's perception of HBD. Of course I also don't know how much material difference it would make as I am simply going by my own "would be" initial impression of HBD, and that is, it is not as strong as a brand as something like USDH which might immediately give people a little more confidence.