What about naming it after something that is famous for using several weapons simultaneously. Drizzt isn't exciting, but what about Marilith Knights ? Girallon Warrior ?
Florentine is certainly accurate (even though it also means a dish served with spinach ), and I would go with it, but I'd have to explain it to my players, which kinda defeats the point
So, I'm going to go with the boring 'Dual Wielder'. Someday, I'll actually make a spicy campaign where I can use 'Spinning Thresher of Drizzit Bane', but till then
Whatever the official name, if the character turns into a killing machine, just call him the "Ronco Vegamatic" (It slices. It dices. It makes julienne fries!)