Why does ‘Pokemon GO Trainer Name’ only show up sometimes on Pokemon HOME?

Question

For Pokemon transferred over from GO, I’ve found that sometimes it selectively shows the name of the Pokemon GO trainer, most of the time not - why is this? Is there a way to retain this?
(I’m not talking about the OT, this is a separate field).

Comments

Also, as a follow-up, does anyone know if moving these pokemon in Pokemon HOME to different boxes (but not to any games, just within the boxes) will remove this effect? Many thanks!

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Does this answer your question? https://bulbapedia.bulbagarden.net/wiki/GO_Transporter#Original_Trainer_and_nickname

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That sorta does, it's the original trainer name who caught it in GO that I care about;

"The Pokémon GO Trainer who sent the Pokémon to HOME is listed on the Pokémon's summary screen in Pokémon HOME. Prior to Pokémon HOME version 2.0.0, this information would be lost if it was moved to a Generation VIII game; this information is now preserved." - does this mean I can freely move my Pokemon from GO to SCVI and back to HOME, and the 'Pokémon GO Trainer who sent the Pokémon to HOME' would still show in the summary page?