Proposing perfume from different brand with same name

I would like to add some body mists from an Australian brand to the database. However, this brand happens to have the same name as a completely different French perfume brand. In this situation, what should be done?

I am fairly certain I've read that the brand is either owned by or exclusively makes products for a parent company, but haven't been able to find any sources for this. Not sure what to do.

If there is any addition that can be made to at least one of the brand names in order to distinguish both brands, we should be fine.

We had the same issue for Memo as an example (both used in France and the Phillipines).

Thank you. I think that should be possible.