In the Rockman ZX Official Complete Guide, Omega's moves have official names. But they're not exactly befitting. I think there might have been an error somewhere, but as it stands, these are the only Japanese Capcom-published names that I know of.
トリプルスラッシュ - Triple Slash
チャージセイバー - Charge Saber
アークブレード - Arc Blade
ダブルチャージウェーブ - Double Charge Wave
Those ones should be obvious enough, now for the trickier ones.
龍炎刃 - Ryuuenjin - What the Brady Games ZX guide calls "Rising Fang" officially shares the move name with X4's special uppercut move from Dragoon, even though Omega doesn't use the elemental version himself.
滅閃光 - Messenkou
裂光覇 - Rekkouha - The ground pound moves. These two are odd. Messenkou from X5's Hotarunicus and Rekouha from X6's Mijinion. Omega's Messenkou is the beam that comes down over himself, and Rekkouha is the 5-directional spread shot. If you know these moves from the games they came from, then you'd probably think it was the exact opposite, X5's messenkou is a spread shot and X6's rekkouha brings down beams of light. I thought it might have been a label editing error, but the pictures and descriptions are consistent in the terminology. They're just weirdly named.
乱舞 - Ranbu - "War Dance" "Boisterous Dance" "Crazy Dance" "Berserker Dance" are some things you could translate it as. Real name of the "7 hit combo" which the guide book describes as a 5 slash combo, followed by Ryuuenjin. Zero can upgrade his combos to 7-swing in X7 and 5-swing in X8, so it doesn't seem too strange.
For funsies, Model OX overdrive move names:
龍炎刃 - Ryuuenjin - With the actual flames this time.
アークブレード - Arc Blade - With iciness.
真空刃 - Shinkuujin - "Vacuum Blade" elec element saber wave.
アースクラッシュ - Earth Crush - Zero's uncharged ground pounding move, the old X2 name instead of the later used "Earth Geyser"
滅閃光 - Messenkou - The next charge level up, attacks at 180 degrees just like its X5 namesake, but more like what Omega calls Rekkouha.
裂光覇 - Rekkouha - Also resembles the X6 version, the fully charged ground pound. These labels are much more accurate than Omega's move names. Strange.