You just use the same phone numbers and accounts and stuff. There’s been standard ways to redirect people to new names for at least centuries.
It costs a couple hundred bucks to start a new llc in most states. People just use their old articles of incorporation and change the names (I know one who just crossed the old ones out with a pen and wrote the new ones in over the top).
Permitting almost always has exceptions for existing operations.
When you close a business on paper you don’t suddenly lose access to services in the name of that business.
If you can figure out a good reason to (any reason counts, restructuring, etc) you can have the same dba filing for your new company, not change anything externally and be fine.
What you’re not considering is that all of the above things might amount to five grand if you live in a particularly restrictive state, but that’s still 45k in tax breaks a year and if there was some reason to restructure internally now you’re getting paid for it.