Hi there – this a super good question that may not have one answer, it depends on timing and also resources and I think you are right to ask yourself the question ‘when is the right time’ to unify the brands into one (if at all).
Are you losing sales right now as a result of not having one brand for all stores?
Is it operationally painful and stressful having 3 different brands for the parts of the business?
What would happy if you rebranded all of the stores? Would you lose customers as a result of not having affinity to the new brand?
What would the ‘staff’ in the stores say and how would they react when / if you rebranded?
There is no point in doing a rebrand, if you actually go backwards and are not better offer. Often people maybe resistant to change e.g. your staff so talking to them about the change, why you want to do it, and when you want to do it, so as to give them a chance for input and engagement is super important to get them on board and supportive – you don’t want the counter. So talk to your team, try and turn it into something they co-own and are a part of – so that they are excited.
One option for you is that you do it store by store, and/or you just start with Online to use the new brand to drive ‘national purchasing online’ as they are typically buying from ‘one virtual store’ and not one of the three actual stores.
Final thing – what most owners have said to me about branding/rebranding is that they never regretted doing a rebrand and getting it into the market, they just think that they could have done better around the timing and sequencing – so having a clear plan and sequence is important.
Good luck. Andy