Two reasons. First, Lloyd’s Brand Guidelines reserve use of the Lloyd’s name, “at Lloyd’s”, and the “Coverholder at Lloyd’s” lockup to approved market participants. Use of these by an unapproved firm would be both a brand-guideline breach and an FCA fair-clear-not-misleading concern. Second, each managing agent’s syndicate brand is gated by that agent’s marketing function; pre-approval use of a syndicate name in a way that implies partnership is not permitted by the underlying carrier T&Cs.
The honest path is to wait, and to publish the relationships at the date the permission letters issue.