Welcome to the forums, @PamPam.
My understanding is that there is only a problem if the names are similar and there is a possibility that customers might mistake one business for the other. If somebody turns up at your site by accident, looking for holistic healing, they’ll know at once they’re in the wrong place.
For example, calmac.com and calmac.co.uk belong to two very different businesses (admittedly also in different countries), but you wouldn’t mistake one for the other. They have co-existed for many years.