。
She calls her younger sister Mina-chan.
Literal
She [topic-は] her younger-sister [object-を] Mina-chan [quotative-と] calls.
The pattern AをBと呼ぶ ('to call A by the name B') uses を for the addressee and と for the name itself — quotative と marking the chosen designation. ちゃん is the affectionate diminutive suffix, common for children and close friends; it softens the relationship and signals warmth, which is why it's often paired with shortened or familiar forms of the name (here, 美奈 → 美奈ちゃん).