The answer to this question depends on how the trademark is used and what level of protection you are looking for.
If the added visual element is a font, it is sufficient to file one application. The brand name will have protection as well. If someone were to copy your brand name in the territory where you own a trademark, you would be able to claim infringement and stop them.
If the added visual is a font and an additional graphical element, for example, an icon, you have two options. You can either register the text together with the icon as one mark. This way, you will gain only implicit protection on the individual elements of the mark, meaning if a third party were to copy them, your claim would depend on the level of distinctiveness these elements have on their own. To increase the level of protection, you can try registering the icon and the text separately. That way, you will gain 100% protection for both.