Yes there is such a betta as a VT DT also known as a long fin double tail. A VT DT more or less looks like a veiltail only with two caudal lobes. The end on these lobes usually are rounded compared to a regular VT that is pointed.
The half moon DT is easy to identify. When fully flared their caudal fin still has a total spread of 180 degrees and the caudal edges are straight not curved like a veiltail.
It is difficult to tell from the photo which your boy is but if his caudal edges are straight then he is a HM DT