Can a marriage status name change include a middle name change?

LOCATION: Utah

I've always hated my middle name, and just recently got the paperwork in order to have it changed, after deciding I would just make my maiden name my middle name.

Apparently I am now getting divorced, which is news to me. I will be changing my last name back to my maiden name, which I've always regretted giving up. Having done this twice in the past, I'm aware that beyond the cost at the DMV and my time, it's free to change a name after a change in marital status.

I'm wondering if I can include either a new middle name, or just dropping my middle name in this "free" name change. Or will I still have to go through the normal paid process to drop my dumb middle name? I want to either drop it altogether, or take a loved one's middle name. I'm not doing this to skip out on legal issues, debts, etc. I've known a few women who did their marriage name change as adding their maiden name to their middle name, or dropping it for their maiden as middle, but this is different than those situations.