"Bāchan" is Japanese for "grandmother", used when the speaker and the grandmother in question are very close. However, when one is referring to someone else's grandmother, "obāchan/お祖母ちゃん" is used instead to acknowledge the fact that the speaker and the grandmother are not related, and it is also a sign of respect, which is very important in the Japanese language.
Her Japanese name (in kanji) is 平野・祖母. In hiragana, her name is ひらの・ばあちゃん. The reason her Japanese name is like this is because, in Japanese, the last name goes before the first name. There is a pause between the last and first names, and this is represented by a "・".