Different LLC needed if move to another state?

Hi, my wife and I are considering to move to a different state. She currently has a NY-registered LLC which she uses to provide esthetician (/skin care) services. The LLC is a disregarded entity so its income and expenses pass through to our personal married filing jointly tax return. If we move to the other state, then would it be necessary or better to create a new LLC registered in that state? And would we need or is it advised to create a new bank account for the new LLC? Or can she continue using the same NY-based LLC? If the latter, then would we need to pay income taxes to New York? We obviously dont mind doing so, and I am just wondering about whether there would be double taxation between the 2 states and any partial offsets through foreign tax credits in the state we move to.

 

We are thinking of moving to Florida, which I believe has no state and city income taxes, so then I guess we'd need to make it clear she was working in Florida through a Florida-registered LLC? Alternatively, we considering moving to another State like California which has state and city income taxes, and so I wondered in this case whether it's advisable to start a CA-registered LLC, or whether the NY LLC and bank account can continue to be used for simplicity and whether the income and expenses would just flow onto our CA and federal MFJ tax returns, and not a NY return. Thank you