Well, it is obviously not true.
He is 11. Does he pray yet? I have an idea: You should make your parents feel guilty for claiming that allah would punish their son for a choice they made. You should also point out that plenty of Muslims have diabetes no matter what their name is, and there is nothing to indicate that changing his name will get rid of his disease.
You should then insist that this is a life-changing decision, and that your brother should pray istikhara before making his decision. Make sure your brother understands that his name will have no effect on his diabetes, and he should only change it if he really WANTS to change it. The rules of istikhara state that after you've prayed about an issue, if you have a feeling that you shouldn't do it, then that is your answer from allah, and nobody should argue with it.
If you can get your parents to agree to istikhara, then you should be in the clear (as long as it's your brother doing it, if they do it then we all know what the answer will be
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