Hi and welcome to the forum.
The H2 come from the code of the module on line 518 (link).
As it look like there is no option to define your own markup (maybe yes, I am taking my first coffee..), you must change it by translating the file.
To do so, first install the core's module LanguageSupport, then translate the module's file :
Once saved, you should be able to see the change on your page.
Did you mean you already added an image field to the system template user ? if yes, then you need to add the permission profil-edit to the user so he can modify his profile. If its not the case, let us know.
If you encounter difficulties, just ask on the forum. Enjoy