There a couple of different badges like racing helmet or racing flag, but there are some badges that I have no idea what are they for.
Like this 
What’s that one means, and how to get it?
Isn’t that part of a gamertag?
The first ones you mentioned are the rewards for completing Star Cards (gamertag Flair). that one in the image is just part of his gamertag, or a photoshop.
No it’s not photoshop and not a nickname. Even Playground developer has one
Yeah same here somebody has a star with an “h” in the middle
i have that star and can uze it…it in your star card…get it all get the star with h…i dont relaly like it…
i want a square with the h in the middle