Chase recently closed my business account without providing any reasons, possibly due to limited activity. They're sending a check with the remaining balance, issued in my old business name, "John's Graphic Design LLC." I intend to open a new business account with a different bank under the name "John's Motion Design LLC." Is it possible to deposit the check with the old business name into the new account?
I'd say the simplest solution is to go to a chase bank and get it in cash, or cashier's check. They might have closed your account, but they still have all the identifying records. You should be able to cash the check, without fee, using only your standard ID. If it's bigger than $10K, that might be a problem, but that problem might be resolved by being willing to wait a few days and sign something.
To keep the integrity of your new LLC, you might want to consider going though all the official motions to defunct your old LLC. In technical terms, you are trying to dissolve one LLC, and then create and fund a new LLC. The "limited liability" part of LLC is what you want to maintain. You don't want anybody to be able to "pierce the veil", as it is called, which means they are seeking redress from the old LLC, but your mixed finances convinces a judge to rule that the new LLC is also liable. I understand that a simple statement of dissolution signed by the officers is all it takes, and you might have to submit it to the state. Sounds easy enough, so I would do it, but make sure to mention in the statement the exact amount paid out to the officers (you) in the dissolution and that it is the entirety of the dissolved equity.
If this LLC is already de facto dissolved, because you haven't submitted any state documents in a few years, that might change things. If you are worried about it, you might want to get specific professional and legal advice at that point. If on the other hand, this is just a simple failed project and you are simply re-branding and trying again, forget about it and I hope you have better success this time.