First of all, I like the design but I do feel like you can check multiple colors because of the checkbox. Even though your image doesn't look wrong to me, the saturation of the border color might look too dull. You could try lime green or light blue with the green check that is centered on the badge.
You could check out this source for a better understanding of radio buttons, which I think is the right way to select a profile badge. Radio Buttons: Select One by Default or Leave All Unselected?
Yes, the first item should be selected as default according to NN group
The main guideline for radio button design is to select one of the radio buttons by default (i.e., when the page loads, in the case of a web application.) This is good usability and elegant design.