New Dex Numbers?

No, they won't.

They're the same Pokemon. There's no reason for them to have a different dex number. It's like asking if east and west Gastrodon should have different dex numbers. Or trash and sand Wormadam.

>>28320815
Nah, they're forms so no.

>>28320870
True but the Alolan forms are something entirely different not just small esthetic changes. They will most likely have a whole new moveset and even history and possibly evolution methods. These are pretty much new pokemon in all but name.

This is also the first time game freak as heavily advertised forms like this.

They won't.

>>28320815
Probably not. It'll be the same in the Pokedex when you've seen a shiny or mega version - you can go to the bottom and choose which form you want to display in the pokedex.

>>28320963
Mewostic M and F both have the same dex number

Precedent is likely not. Shellos/Gastrodon have regional variants that share dex numbers, formes share dex numbers, gender differences share dex numbers.. Nidoran M/F are the exception to the rule by virtue of coming before all the complexities of Gen III and onwards.

>>28320963
>This is also the first time game freak as heavily advertised forms like this.
bro formes have been getting hyped since Deoxys

Wormadam, Deoxys, and Meowstic are notable examples that come to mind of Pokemon that share dex entries but have different forms that have different stats, types, abilities, and/or learnsets. The only curious new dex-affecting element will be alola Vulpix presumably evolving via a different method.