If I am on probation and a detective investigating a case involving my cousin not me asks me my cousins last name do I have to tell him

I am sure any good detective will find out what the last name of the person is anyway with or without your help.

No you don't have to tell them, but then they can report this to your probaton officer that you may be involved in the crimial activiy.

And since it sounds like you are a minor child, the courts look at this differently than in adult courts

Even you or your cousin do not disclose this info, they have a way to find out anyway.

No.

You have the right to remain silent , Way too many people don't use this right and end up in trouble . Also , its OK for cops to lie but if you give a false statement you could get in trouble