happy day, happy time

do you still remember our old promise?

Hitsugaya and Hinamori's origin traces back to Junrin'an, a rural area within the West District of Rukongai. Unlike the majority of Gotei 13 members, who were born inside of Seireitei (a.k.a. Soul Society's central city), Hitsugaya and Hinamori certainly didn't lead what we'd call a "luxurious life". Nevertheless, Junrin'an was still a paradise compared to many: neither was it a neighborhood of violence (think about Kenpachi and Yachiru), nor was it a showcase of absolute poverty (think about Gin and Rangiku). As a result, Hitsugaya and Hinamori were able to grow up as a bright pair, fully stocked with sweet childhood memories.

Yet all happy moments would eventually come to an end. The quiet life of little "Shiro-chan" Hitsugaya and "Bedwetter Momo" Hinamori was suddenly rippled by the latter's ambition of becoming a Shinigami. After making it into the top class of the year, an excited Hinamori bid farewell to her little friend at Rukongai and left for her next stop in life: Shin'ou Reijutsuin, the school of all Shinigami wannabes. It was during the same period that Hinamori developed a blind admiration for Sousuke Aizen, whom she talked about non-stop in front of little Hitsugaya upon each of her return from school.

Shortly before Hinamori left for her first day of school, she made a quick promise with little Hitsugaya:

If you were ever able to enrol into my school,
I'll start calling you properly by your last name!

(Note: not only is Hitsugaya's petname "Shiro-chan" an informal but cute title, there's a bit of tease in the suffix -chan, which is used more often on girls or little children)

Although Hitsugaya rejected her offer immediately by claiming that he doesn't care about the School of Shinigami at all, everything happened after the said incident can only be left to speculation at this point.

Source

• Manga: The Untold Stories, Volume 15
• Anime: Episode 46