Is there a regulation against putting your rank on your bag?

AR and DA PAM 670-1 comprise of 398 pages of what you WILL wear and what you MAY wear. If the reg had to state every instance of "WILL NOT wear" it would be thousands of pages.
If you cannot find it stated as "will wear" or "may wear", then it is against regulation to wear it.
Rank on a backpack is not stated as "will wear" or "may wear" in either publication

There is no regulation that will cover what you are allowed to wear on your personal time. As long as it is not offencive, you may wear whatever you want. Since you are in the National Guard this rule is even less strict then it would be on active duty.
If you are wearing a personal bag while in uniform then the regulations are fairly specific about what you may wear and how it will be worn. If you are unfamiliar with the regulation, then you should pull up your Google box and open DA PAM 670 - 1 and AR 670 - 1. Regulations are the bases of everything we do, so you should familiarize yourself with them early on in your career

I would probably not worry about it, unless the unit asks that you take it off. I mean, it's not like you are putting corporate logos or something inappropriate on it. Also, the medium rucksack I was issued has a big velcro area that people were putting US Army/name/unit patch/rank, or a combination of the 4 on it and it was not an issue.