I am not sure how your business can get recognized as an international brand. Reviewing your profile, it looks like you are providing personal eye care exams, prescribing contact lenses and rendering a very localized personal type of service. I cannot think of any brand names inside or outside of the United States in the eye care business. The only one that comes to mind is Bausch and Lomb which sells eye care products. Therefore, this is an enormous task for a business of your size in your respective industry.
However, if you truly believe that your business is very exceptional with its service and business model compared to everyone else in your industry, then you might want to consider a franchise model. A franchise business model is a business that is doing very well and wants to expand to new markets outside the local geographic area. As the franchise grows, it becomes a recognized brand over time in new locations. There are plenty of examples of this in the food industry – namely McDonald’s which sells hamburgers all over the world through a franchise model. It is a very well recognized brand internationally.
The challenge for you is to create a very profitable and stable business that is highly replicable, complete with training and support for someone wanting to open an eye care business using your business model. Otherwise, you will have to do this on your own, location by location and most locations outside of your country most likely have existing eye care clinics. Therefore, you need to make sure you can truly offer something different and exceptional compared to what the competition is currently providing.
Most businesses that have become international brands (Coke Cola, Apple Computer, Disney, Samsung, etc.) attracted lots of customers by offering something that was great and there was nothing like it in the marketplace. This is how you become an international brand – go deliver something that thousands of people fall in love with that is different and outstanding. This is what is required if you want international brand recognition and, in my opinion, I do not think a global branding strategy fits with your particular type of business given your current size, location and what is truly required to make this happen.