Will identity theft be erased from my record after a certain period of time or what can I do to make it so?

They do not automatically get erased. You have to file a motion with the court to have them expunged. The motion must convince the judge that it is in the interest of justice to have the charges removed. This can be done pretty easily be any attorney. It is something that you can also do on your own, but if you don't know what you are doing the odds of succeeding are low.

You can try an expungement but make sure you penal code section is not on the list of non-expungible crimes.

Your question is unclear, but if you went to court and were placed on probation the case never goes away, there is no way to expunge a criminal conviction. They can always be used as prior theft convictions to make a petty theft a felony with a prior, city, county , state or federal employers must always be told about the conviction. You must also tell licensing boards like the state bar, medical licensing, nursing, lottery sales. In addition if a background company checks they will find the conviction in court records. It may have less effect as time goes by, but it will still be there.