Absolutely. An attorney should do the best job they can to defend you regardless. Some attorneys do not want to know if you are guilty because it can limit their options, primarily in making a determination as to whether a defendant should testify or not.
Your attorney is either a defense lawyer for you, that you can trust with all of the true facts of the incident, or you need another lawyer. One of the worst mistakes you can make is to hire a lawyer, entrust the lawyer with your defense, and then mislead the lawyer by not telling him everything. Good luck.
This response does not constitute legal advice. Given the nature of this website, it does not create an attorney-client relationship. This answer is provided solely for informational purposes, for you to use as a starting point when speaking directly with a lawyer in your State. If you do not trust the lawyer you have, I urge you to immediately contact and retain another experienced criminal defense lawyer admitted to practice law in your State before you make any decisions about this case.
It is very important for you to tell your attorney everything you know about your case (the good, the bad, and the ugly). I always tell my clients that no one can help them more with the truth than their attorney. However, I understand your hesitation. If your defense attorney knows you are guilty, you think it might be harder for them to fight through all obstacles to get your case dumped. You need to decide whether you trust your attorney or not. Their number 1 duty is to zealously fight for your rights and defend you. All that being said, it is extremely hard to effectively defend you if they have a blind eye to all the facts of the case.