Definitely not. You’d be totally misrepresenting yourself and would be exposed to subsequent liability (or even fraud) issues. It’s actually illegal in California to file a DBA with a corporate marker like ‘inc’.
Inc, Incorporated, Corp, LLC, etc. are reserved for specific registered entity types. If you submitted a Fictitious Business Name application with one of those appended to the name, my guess is that you’re application will get a nice denied stamp on it.
The only time that might be possible, is if the filing entity is a corporation, but I’m not even sure about that, because usually you have to file it in a manner similar to “XYZ, Inc. doing business as Joe’s Hot Spot”.
I’m not 100% sure about this but I think it’s a fair assumption that ALL states prohibit the use of inc/corp/llc/ltd, etc unless by a legit corporate entity of the suggested type.
It’s not just part of the name, it really means something. I get so many inquiries from people who want to sound important so they call themselves CEO’s and add ‘inc’ to their name. I look them up (easy) and can immediately tell that they are bogus.