
Source:
Small Business Administration
"A fictitious name
(or assumed name, trade name or DBA name, which is short
for "doing business as") is a business name that is
different from your personal name, the names of your
partners or the officially registered name of your LLC
or corporation."
"For example,
let's say Mary Smith is the sole proprietor of a
catering company she runs out of her home. Mary wants to
name her business Seaside Catering instead of using her
business' legal name, which is Mary Smith. In order to
use Seaside Catering, Mary will need to register that
name as a fictitious business name with a government
agency. The appropriate government agency depends on
where she lives. In some states, you have to register
fictitious names with the state government or with the
county clerk's office; however, there are a few states
that do not require the registering of fictitious
business names."

Each state has it's own requirements, but here in CA
we have to first, be certain the name we want hasn't
already been registered, then we have to file the
paperwork (available on the county web site) and pay the
fee (it's around $30 here in Contra Costa County).
Before it's official, we have to take those documents
from the county to a local newspaper for publication.
The county will give you a list of newspapers to choose
from, how long they ad needs to run and the paperwork to
give them.
This step needs to
happen before you can open a bank account.
Before filing for your Fictitious Business Name,
check to see if the domain is available.
No sense having a business name but not being
able to register the domain name.
Sometimes the domain name needs to be something
"close" to the legal name vs. exact name.
Here is a
listing by state from the Small Business
Administration that will tell you the document name and
filing requirements for applying for your Fictitious
Business Name.
You may also want to check
into trade marking your name as well.
United
States Patent and Trademark Office
How to Register a Trademark for a Company Name