The reason, I believe, that Mazda is officially dropping the Miata name is for consistency across its product line. Mazda, with a few exceptions, has always used alphanumerics for its model designation in the U.S. Note: R100, RX-2, RX-3, RX-4, then RX-5 Cosmo (a revival of the Cosmo 110S sports car that was Mazda's first rotary model), plus 808, 626, even the GLC, even if it stood for "Great Little Car." The prefix "RX" has always meant "rotary engine" in Mazda-speak.
(Side note: Mazda was named after the family name of the company's founder, Jujiro Matsuda. In their ever inscrutible way, the Japanese named the company Mazda because (a) it sounds like Matsuda pronounced Japanese-style and (b) Mazda is the Zoarastrian god of light. Long ago GE used it as a brand name on light bulbs. True. You can look it up).
Anyway, the Miata, when it was introduced was the MX-5 Miata, but was called the MX-5 everywhere but the U.S. And the name was fine, except that it had little carryover to the rest of the line. People knew that the car was a Miata, but didn't know that it was a Mazda. So while it was the top selling sports car in history (again, you can look it up), it didn't have any coattails for the rest of the Mazda line.
So now Mazda will slowly wean the MX-5 from its Miata moniker and hope that MX-5 and RX-8 have some resonance with the Mazda3, Mazda5, Mazda6, etc. Speaking of which, I feel silly saying Mazda Mazda6. Whose idea was THAT anyway?