To begin with, don't create from scratch, import a wonder card then edit the valid details.
What you mentioned doesn't hold true for all generations, but at least for Gen 5, language for Shiny Genesect HAS to be Japanese, as we know it was only distributed locally, and local distributions for Gen 5 restricts the language that can receive it. However, PKHeX likely doesn't flag it, because that data isn't on the Wonder card. We know that it was distributed only for Japanese cartridges locally, but that data isn't written on the wonder card, so they can't track it. [Also note: Gen 5 does not have region data on it. Region data was only implemented starting with 3DS era]
Past Gen 6, it can have any region data on it, simply because it can be transferred up on any region 3DS, regardless of the language of cart. Just know the language doesn't change.
(Technically, the wonder card itself shows Genesect can have any language and languaged nickname as per the receiving party, but we know it can only be Japanese, as it can only be received by a person with a Japanese language cart. Think of this as metadata; data beyond actual data. We know this in real life, but it's not noted down as data on the wonder card.)
The label has nothing to do with region settings. It's purely for language.
Don't confuse language and region settings, partner.
Name changing: Unlikely. Name changing probably only occurs if it had an illegal nickname, but event mons typically can't be nicknamed by the player, hence it cannot gain an illegal nickname that would result in its name being fixed.
Not to mention if it did have an illegal nickname (who knows how), it would already be fixed in Transporter -> Bank, which that transfer uses the language of the mon itself. So there wouldn't be a chance for it to be fixed in Bank -> HOME.
(FYI, for such a name fix in HOME, would likely match language settings of HOME, not region settings. Region settings practically influence nothing in a Pokemon's data.)
[I reckon the story where you heard the shiny Genesect's name being fixed, belong to a badly hacked shiny Genesect, that was hacked into Gen 6, Gen 7, or Gen 8 (past the Transporter->Bank) stage]
Why not being flagged? already explained.
How does it change names? for events extremely unlikely, but if it does: already explained.