The police may want to make sure they are arresting the right person. If they ask you to identify yourself, tell them your name. That is the last question you should answer that is asked by the arresting officer, by a police detective, or by any other law enforcement officer prior to your booking. In response to any other question, respond politely but firmly that you will not answer questions without having a lawyer present.
When you are booked into the jail, a booking officer will ask you questions while filling out a booking information form. Most of those questions (such as your height and weight and identifying tattoos) are safe for you to answer. You may not want to reveal your address if there are drugs or other evidence of a crime at that location and if the police did not arrest you there. You should answer questions about medicines you are taking, especially if you might need those medicines while you are being held in custody, but you should not answer any questions that might link you to illicit drug use. If you think you need drug treatment or might need help withdrawing from a drug, tell that to your lawyer, not to the jailer.