If you mean an office where they are physically located, with their name on the door, a telephone number, fax number, etc., yes, they generally have an office location. This is not required; however, and some lawyers operate virtually, leasing or renting office space on an as needed basis, e.g., for meeting with clients or meeting with other lawyers and their respective clients on a particular case, but are mainly based out of their home. It's harder to see clients this way, and most clients like to see that there is an office that the lawyer works out of, around other lawyers, and support staff. It would be had to meet with company representatives charged with investment fraud, individuals charged with serious crimes such as murder, aggravated sexual assault, possessing and distributing large quantities of narcotics in a temporarily rented office space or in a coffee house or restaurant. These clients want to see an established lawyer with an established practice and a proven track record before they would hire such a lawyer. Similarly, a divorce case with a large estate to divide or custody of children that is contested, want to see similar surroundings and establishment.
If you are asking if they have (or hold) an "office" as in a title, then all lawyers are sworn in and take an oath prior to being able to practice law and are, hence, officers of the courts before which they practice. This awards them a different recognition, obligation, and duty of which they must maintain a higher standard than a non-lawyer. This raised standard applies in life, in general, and especially when before the bar (court). They are also held to a higher standard if a Rule of Professional Conduct has been breached and are punished more severely when they breach any of the other standards which they have taken an oath to uphold. If a criminal law has been proven to have been broken, they generally receive harsher punishment for having broken the law which they are sworn to uphold, pejoratively affected (degraded) the profession, and caused the loss of public confidence in the legal profession as a result of their actions.