You can do either, but in general I hate changing the corporation name after you already have contracts in place etc. It isn't a huge issue, but to do it properly you need to update all agreements with a notice of the change and make sure all parties are updated. Then you also have bank accounts to deal with, credit accounts if any exist etc.
A lot of times a DBA is easier and even more appropriate, especially if what you are doing is brand specific. And at the bank you can just add the DBA as an additional name on the corporate bank account and deposit checks that are written to the DBA etc. Plus with the DBA you are not required to change any current agreements etc.
There are reasons to do both honestly, the earlier you are the more I personally would lean towards changing the corporate name, the further along you are I'd look more towards a DBA unless you have really good reasons to change the original corporate name.
Just as a point, most brands are not corporate names, e.g. look at Proctor and Gamble etc, they have 100's of brands under their corporate umbrella and most are not their own corporation or even a DBA, just a protected brand name. Even Google is no longer Google per se, they are Alphabet with Google as a core brand.
