Currently only way to add a Branding Theme to an invoice via API is by specifying the BrandingThemeID parameter.
This is rather impractical as BrandingThemeID has to be unique across all of Xero, so if you hardcode the ID for your real Xero organization, when you go to try something with your demo organization, this will fail as ID is not the same, even if the name is.

On the other had Xero already forces you to have unique names for your branding themes, but these are supposedly only unique within your organization, so you could have a Branding Theme with same name in your real organization and your demo organization.

My proposal is to allow me to specify a Branding Theme I want to apply to an invoice either by ID or Name, as both should be unique enough so there is no confusion which theme should be applied. This would make working with the API a lot easier.

Another reason is that Xero doesn't expose the ID of the theme anywhere in the UI, making it rather difficult to get someone to tell you what their theme ID is, as they simply have no clue. They only see the name.
There are workarounds for this issue, but this would also be much simpler if we could just specify the theme by name in the API.