Yes but these things have strict time limits. Contact a locally experienced criminal defense attorney ASAP to evaluate your case and hopefully not just tell you what you want to hear in order to gain your business.
Assuming the arrest was lawful and the test was accurate, you may have an uphill battle to "beat" the case. But with a quality locally experienced criminal defense attorney at your side you give yourself the best chance to get the best outcome possible given the facts of your case....even if all that can be done is obtaining the minimum sentence under the law which is 96 hours jail (assuming the prior was within 10 years, possibly with alternatives to actual jail), a fine of around $2,500, an...
Go to court and, assuming the court agrees you do not have the ability to retain an attorney, an attorney from the Office of the Public Defender will be appointed to represent you.
Since the charge is a misdemeanor, an offer likely will be made by the prosecutor to settle the case at the first court date. If you accept the offer then you will be sentenced soon after pleading guilty and will likely be placed on summary probation to the court for 3 years, be ordered to pay a fine, et al. If...
Assuming you are eligible for an appointed attorney, go that route for your arraignment (first court appearance) and see how you feel.
The main concern you should be having between now and the first court date is what to do about DMV. You need to request your administrative hearing within 10 calendar days from your arrest to preserve your privilege to drive.
Might make the most sense to hire a quality criminal defense attorney to handle the DMV hearing at least.
The bigger issue is the ID in court, not so much the fact your name was not on the police report. If you have a lawyer, ask him/her. If you don't trust the lawyer you originally hired, perhaps it's time to hire the best, locally experienced, criminal defense attorney you can afford.
A lot will depend on the attorney you hire, and the courthouse where your case will be heard. Stop worrying and speculating and hire yourself a quality, locally experienced criminal defense attorney ASAP.
You can still be charged under Vehicle Code section 23152(a) (Driving Under the Influence of Alcohol &/or Drugs), and in some instances Vehicle Code section 23152(b) (Driving while having .08 or higher BAC).
The .05 helps your case, particularly if no drugs were involved, but in the event you wish to be reactive instead of proactive and wait and see what, if anything, is filed THEN hire a criminal defense attorney, so be it. However, it is always advisable to be proactive.