From the name alone, you wouldn't have known that it's a name of a villainous group from gundam_00 except if you read the wiki. The word "Innovator" itself is so generic it has a disambiguation page on Wikipedia (and searching for "innovator" would redirect you to Innovation).
Japanese has it written in katakana without the plural "s", but usually most such similar names for organizations get pluralized when translated into English (because the singular form sounds clunky), and IIRC most English sources spell the Gundam 00's organization イノベイター as "Innovators" (with the s) in English.
As for the qualifier, well, no harm done adding two more numbers to make it truly unambiguous.
Otherwise "innovator(s)" may possibly conflict with other Gundam names down the line. Also, innovator_(gundam) alone may cause people unfamiliar with Gundam 00 to assume it's a character name, a mobile suit/weapon (whether an actual Gundam or not), a ship or flyer or some vehicle, or a weapon... from who knows which series.
Those two numbers will make it far more future-proof.
Edit: On the subject of Gundam qualifiers in general... I'd say that _(Gundam) alone is a poor choice most of the time because of the sprawling nature of the series with multiple spinoffs (and subseries with their own spinoffs, and then spinoffs on top of that), plus the proclivity of vehicle chartags (that sometimes might sound like character names, like Penelope). To make it worse, "Gundam" can be confused for the series as a whole, a specific series (e.g. Mobile Suit Gundam), mechas (referred to as "mobile suits" in-universe) called Gundams and mechas not called Gundams. So here's what I recommend:
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Qualifiers should generally only be used when necessary (i.e. potentially ambiguous), instead of blindly applied gacha-style.
Anything that is a "mobile suit" gets the _(mobile_suit) qualifier.
Anything that is a "mobile armor" gets the _(mobile_armor) qualifier.
Any other vehicles or weapons get the generic _(Gundam) qualifier.
Characters and organizations get the specific series qualifier. (e.g. _(Mobile_Suit_Gundam)).
Any mechs with Gundam in their name doesn't need a qualifier... unless it's potentially ambiguous with the name of their series.
Avoid using serial numbers for disambiguation (whether as a prefix or qualifier), because it makes searching/tagging harder and require people to look them up. Main exception being the RX-78-2 (the 'original' Gundam), because most people in the fanbase know that specific serial number and will use it to disambiguate from all the other Gundams (mechs, series, etc.)
SD Gundam 'mechs' get the _(SD Gundam) qualifier because otherwise their names have a high possibility of colliding with main series mech names. A lot of the time it's the exact same name (or a slight variation) written using punny kanji instead of the original katakana.
The above system was what I came up with while working on Ishiyumi's G-Spring Goddess series, which feature many obscure mechs that require their own chartags and qualifiers. I started with just _(Gundam), then the whole thing turned into a complete mess (especially with SD Gundam conflicts). So I took a look at how some existing Gundam tags are qualified and noticed _(mobile_suit) and _(mobile_armor) being used for a decent chunk of them. I then adapted this into a 'systematic' approach and renamed the chartags I created.