Holden's brother D.B. is not referred to by his full name in the book or in any interpretations or reviews of Catcher in the Rye.
It could be suggested that the older brother is referred to only by his initials because he is a writer. And, just like J.D. Salinger, initials are used. Or, the initials could make him a remote, distant character to Holden, who feels that his brother is a sellout because he writes scripts in Hollywood instead of serious books.
Or, D.B. is referred to only with initials, because he is an adult, and out of Holden's world, so therefore, he is more phony if he does not have a full name.
As far as I can tell, from all my research for this book, D.B. is never named.