Under normal circumstances, credit cards should never be lent to anyone, but it is normal for ordinary family members to use them. You just need to know the password. You can sign your name at will, or you can sign your own.
Personal advice to you: If you know about credit cards and can use them well, there is no problem. If your personal control ability is poor, or you hide it from your mother, it is not recommended that you use a credit card, because credit cards are related to personal credit problems and will involve many problems in the future. Don't drag your mother into trouble because of simple irrational consumption or debt.
If you don't understand, please ask. If you are satisfied, please adopt it.