Let us say ...

Mabel has operated a diner from a building near the road on her property for a long time. It's called Mabel's Kitchen. The business entity started as a sole proprietorship - Mabel Smith d/b/a Mabel's Kitchen. She never registered the DBA (Doing Business As) nor the trade name.

Now Mabel is getting on in years and her children now handle most of the work. Also, much of her business is now coming from catering & online sales of "Mabels" branded products. For these and other reasons Mabel considers incorporating the business but finally decides to form a trust - MABEL'S KITCHEN TRUST - on 2/19/2015.

Now on 2/20/15 everyone arrives at the diner and told the business entity has changed, but she doesn't change the restaurant signage and continues to answer the phone as Mabel's Kitchen. That's the trade name the new trust will continue to use. The business continues to use the old bank account seemingly without any issues.