YOU SAID:

My Cat is named the same name as my grand mother.

INTO JAPANESE

私の猫は私の大母と同じ名前です。

BACK INTO ENGLISH

My cat has the same name as my great mother.

INTO JAPANESE

私の猫は私の偉大な母と同じ名前を持っています。

BACK INTO ENGLISH

My cat has the same name as my great mother.