The act of giving a false name is not a crime by itself, it needs to be in connection with some other facts. For example, giving a false name during a traffic stop would constitute False Information to a Police Officer (ORS 807.620, not your facts).
If you gave a false name in order to avoid be arrested on a warrant that would be the crime of "Giving false information to peace officer for a citation or arrest on a warrant," in violation of ORS 162.385 (2). That crime is an A misdemeanor, which means maximum possible punishment is up to a year in jail and a fine of $6,250, in addition to whatever you have coming to you on the probation violation.
If you simply gave a false name and that was it (i.e., you weren't on warrant status), then you might not have committed a crime at all. You should talk to an experienced criminal defense attorney to get a better handle on your rights in this situation. Do not take a plea without first having reviewed the police reports carefully with your lawyer. If you are unhappy with your court-appointed attorney there are plenty of private defense attorneys who would be interested in a case like this.
Also, you may or may not also have a potential civil suit for police brutality depending upon how they justify or explain their use of force. Even if you have valid grounds for a suit you have to find a personal injury attorney who is well versed in all the nuissances of these types of cases, which require, among other things, that you document your medical expenses, that you provide the county, the sheriff, jail administration, and the officers sufficient tort claims notice (i.e,. written notice of intent to bring suit within less than 6 months of the acts occurring). Talk to a personal injury lawyer.
This post is offered as general information and is not intended as legal advice. This information does not in of itself create any attorney-client relationship.
The crime that sounds closest under the circumstances sounds like Giving False Information to a police officer. This is a class A misdemeanor with a maximum penalty of 1 year in jail. Most courts consider both the circumstances around the incident as well as your criminal history in determining a sentence. This assumes that you are actually charged and convicted, which there is no indication of. You should consider seeking an experienced attorney who deals in both criminal defense and civil rights violations based on your injuries sustained while in police custody.
*Nothing in this comment should be construed as legal advice and should not be summarily relied upon as such. This commentary does not create an attorney-client relationship. For specific legal advice about your case, it is best to contact a lawyer to discuss your particular case.