Azuki-chan(1992)

Azuki-chan is a manga series about a young schoolgirl named Azusa Noyama, nicknamed Azuki-chan because when she was younger she was accidentally called Azuki instead of Azusa.

She always hated the name until one day a new boy starts in the same class as her called Yūnosuke Ogasawara, the same day she is teased by a boy called Ken-chan about her nickname. Yūnosuke-kun passes by and happily memorizes the name becoming the first girl he notices. Azuki is over joyed, and instantly falls in love with him, loving both him and her nickname.

However Azuki gets jealous when she sees him chatting to other girls and cannot work out why he doesn't realize her love.

(Source: Wikipedia)