The questioning of this issue is the wrong way round.
Andrew holds the title Earl of Inverness, that much is true. It’s also true that is is common usage for titled people to use their title in lieu of a surname, even when they do actually have a surname. Like Emma Thynn, now Marchioness of Bath, but who competed on Strictly Come Dancing as Emma Weymouth because at the time her title was Viscountess Weymouth (her husband had not at that stage inherited the title Marquis of Bath).
So if Andrew holds that title, by custome and practice he is entitled to use that name. So it’s not false information, even if he doesn’t use it often, or even if this is the first time he has used it.
The question then should be what are Companies’ House requirements for company officers and the names they use on the register? And has Andrew breached those rules by using the name Andrew Inverness?
I have looked on Companies House website but they don’t deal with this. It will be an issue of their practice, not strict law, because you don’t need to follow a legal process to start using a new name. This might surprise you, but it’s true. If you want to get a driving licence or passport in a new name, you’ll need a deed poll, but people’s names change over time, and people may validly use different names at different times, and that’s not generally an issue.