Highly doubt they'll drop the Pokemon saying their names.
That said, there are plenty of Pokemon who just have monster roars in the anime (Charizard, Salamence, Tyranitar, several legendaries) and the Paradoxes can easily just have those.
Or alternatively, since the Paradoxes are derivative of present day Pokemon with normal names, they can just say their present day counterpart's name. Like Great Tusk and Iron Treads will both just have "Donphan" as their cry, Brute Bonnet will just say "Amoonguss", Iron Hands will just say "Hariyama", etc. After all, the Paradox names aren't really their names but codenames by scientists given to currently unidentified and foreign Pokemon.
Koraidon and Miraidon had the two word naming trend most Paradoxes do in canon once upon a time before they got their real names, Koraidon and Miraidon, after all.