Dissolving the LLC would require starting over with a new entity, which can be more time-consuming and may reset any business credit you've already established.To change the name, you can file an amendment with the Wyoming Secretary of State, which is straightforward and keeps the LLC intact while giving you a fresh identity.

I use tenantbackgroundsearch.com, although many of the vendors provide automated reports that are nearly identical. 

Would we be able to put the home in the Holding LLC since our names are directly on it (albeit a Delaware LLC meant to hide our identities)?

@Darrick Lowe, We just had a situation nearly identical to this-  Eastern PA.

Then there's the issue with doing a 1031 which is fine but my property taxes would go from $2200/yr to $4400/yr for an identical home. 

Be sure you have verified their identity prior to sharing any sensitive information.Here’s the IRS article for further information.Have you had any of these scenarios happen to you?

We are trying to sell two identical buildings separated by an enclosed courtyard.  

Scammers are premeditated thieves..

Using a VA loan for a second property, where I’d move in and rent out my current home.When I made an offer on a fixer-upper (I didn’t win that bid), the loan officer mentioned it might be difficult to convince the underwriter why I’d need another VA loan for a second property in the same area, especially since the new home is almost identical to my current one (same size, age, school district, etc.).

Identical situation happened to me so I went to a new lender 2 weeks before closing and everything went perfect.