Answer your question. First of all, this card is yours, and other uses are not allowed according to bank regulations. But there is nothing wrong with using it in real life. As for the signature, it must be your signature. Because this signature should correspond to the Chinese phonetic name on the front of the card and be consistent with the signature handwriting on the blue of the personal signature on the back of the card. But in some cases, the cashier won't check the handwriting at all. Generally, they think the password is correct. However, comics without consumer passwords often check their handwriting carefully.
Here's a suggestion. Your card may be used again in the future. If you sign your name on the back of the card, it will remain unchanged for others to use in the future. Therefore, you'd better help your family to apply for a negative card, which is more convenient and safer.
I hope my answer is helpful to you, thank you!