lawnlubber is right.
It is not necessary to have a dba. The dba will just notify your county's tax accessor that you are in business and will look forward to receiving taxes on your equipment, etc.
To get around the bank situation, lets say your name is Joe Smith and your company name is XXX Lawn Service. Do all of your advertising as XXX Lawn Service.... and don't have "your" name on the advertising. On all of your proposals, invoices, statements or whatever you plan to use, have the company listed as Joe Smiths' XXX Lawn Service with a note at the bottom stating that all checks are to be made out to Joe Smith. There is no law stating that just because you own a business that you have to have a business account. The bank wants you to open a business account so that you can pay them a service charge every month!
In Texas (or at least Harris County), when you file a dba they will tell you if someone else already has that name on file. And all anyone has to do is say OK, I want that name too and they will take the $11 filing fee and now 2 people have that comany name.