Andy,
Checked quite a lot of Flybe entries in MyLog and it would appear that whether ID is shown or not isn’t relevant to newer aircraft or earlier/later versions of RB software.
Logs for every aircraft showed ID for some flights and not for others over a period of a few months.
Is it not more likely to be a matter of the crew deciding whether they're going to input ID or not? If that is the case, presumably the company doesn't have a fixed policy.
Syd