There are two different cases. If you are replying an ad that is hiring then you will be sending them your resume instead of posting it on the craigslist. In that case if you are not comfortable giving your personal information you can take your address and phone number out of the resume and just leave your name and email address. If they are interested in you, they would contact you for the next step. Although it depends where you are applying. If it really turns out to be a big corporation their HR department may want to see full information on resumes. Its up to you to evaluate the situation and send the right kind of resume to right company.
The other case is you are posting your resume on craigslist and waiting employers to contact you. In that case you do not put there your phone number and address. You of course should add your name there . I dont think a harm would come from adding your name , using only your first or last name may be ok too, but there needs to be a name , otherwise people either will think you are too secretive or they just simply wont know how to address you while making a contact.
At the end , use your common sense. Giving out name or cell phone number (if you are using) is usually considered ok since name is meaningless just by itself and cell phone numbers can easily be replaced. Giving your address, social security number or any financial information is dangerous since they can be abused, and so on...
“Do not judge, or you too will be judged. For in the same way you judge others, you will be judged, and with the measure you use, it will be measured to you.
“Why do you look at the speck of sawdust in your brother's eye and pay no attention to the plank in your own eye?
How can you say to your brother, ‘Let me take the speck out of your eye,’ when all the time there is a plank in your own eye?