The J-11D's "D" and J-16D's "D" denote different things.
The "J-16D" is not an official designation, it's one given by PLA-watchers. The PLA themselves usually change the prefix of their designations to denote special missions, e.g. JZ-8F instead of J-8ZF. Therefore, the official designation given to the "J-16D" when it enters service will probably be something like JD-16.
The "J-11D", while technically also an enthusiast-given name, is much more likely to be the final designation because it follows all precedence set by the PLA.