Which is correct?
- This is Dr. Yang Jeng-Tze, professor of entomology.
- This is Dr. Yang Jeng-Tze, a professor of entomology.
Since OP's context isn't "...of entomology at some establishment" there's no reason to be concerned over whether the establishment has more than one professor of entomology.
Having said that, if our professor really was the only one then even if that was the context, he'd obviously be introduced without an article. But in a context where that distinction doesn't need to be made, he can still be introduced without the article, which is slightly more "deferential".
Consider, for example...
...where we don't know or care where she teaches, or whether there are any other teachers of penmanship there. Adding an article there would detract from Miss Smith's social status, I feel.