Often instead of the name, siblings say "big brother" or "big sister", even when they are grown up. You can even use this to other people as a polite term. And
Didi is pronounced as Dee-Dee.
Of course "Di" could be used as part in Chinese names, but then it does probably not mean "brother". There are many Chinese words which look similar in pinyin but have totally different meanings, which is seen when you write them in Chinese characters.
"You sought a flower and found a fruit. You sought a spring and found a sea. You sought a woman and found a soul. You are disappointed."
"It does not become me to make myself smaller than I am." (
Edith Södergran 1891-1923)