I worked with my insurance agent and obtained an umbrella policy in addition to the dwelling policy I obtained for my rental.As a sole proprietor, however, is it worth it to operate under a business name rather your own name (i.e, DBA filing)? 

Kevin, welcome to BP, I just joined too...I would get the business off Schedule C (assuming you're a sole-proprietor minimizing taxes), get a free EIN, start a LLC, and put those handyman revenues right into your entity (maximize profits) while building and seasoning your business.You want to get a dozen trade lines reporting while paying them off immediately every month and get to 80 business credit and 720+ personal credit. 

Schedule C if you a sole proprietor) & you do not have any w-2 employees working for your self-employed business or otherwise.2.

I'm just starting out investing rental properties out of state and I keep going back and forth on whether to structure it with a sole proprietor with umbrella insurance or starting an LLC in the state I plan to buy properties in.

If you told the IRS you were a sole proprietor then you file the LLC income as a disregarded entity for tax purposes on Form 1040 Schedule E.

If you have an LLC that only has one member, chooses to be taxed as a sole proprietor, and does not file it's own tax return is what is called a "disregarded entity". 

Hi, so I'll be buying my first rental property as a sole proprietor very soon and have a couple of questions.1.

Sole Proprietor is also a pass through entity.  

Imagine thousands on businesses deciding to conduct business as sole-proprietors and partnerships instead?

Google: Sole Proprietor's status as a covered employee for a state form where a declaration can be made about Workman's comp.