Thank you for the information, however, I am unclear on exactly what you mean by "clear your name." If you are asking if the employer can be forced to change their opinion of the facts, then the answer is, no. However, there are a few circumstances where this conflict in perception of the facts and who was responsible for the ending of your employment, might create a legal issue.
The first is if you were to need to file for unemployment benefits. If you were denied benefits because the employer says you abandoned your job or voluntarily quit, then you could appeal that determination and then both you and your employer would have an opportunity to present your side of the facts and let an administrative law judge decide what they believe the correct legal conclusion would be. I can't guess how that would turn out without having all of the facts, including those from the employer's perspective. But, that would be your option in that case.
The other issue is if your former employer were to respond to a request for information about your employment by a prospective employer. If they told them that you abandoned your job, and that cost you a job offer, then you could, if you choose, file suit for defamation of character. The former employer would have to present facts that supported job abandonment or they could be held liable.
But again, just making this decision because that it his opinion is not something you can force him to change. You can only react to one of the issues I mentioned above in the ways I mentioned. If you can convince the triers of fact that you had permission to be off and did not abandon your job, then you will prevail.
Please feel free to ask for clarification if needed. If none is needed, the if you could take a moment to leave a positive rating in the ratings box above, I will receive credit for assisting you today.