Small business owners- depositing checks with your business name- how exact must it be?

Let me know if you have personal experience with this- that means you small business owners (large too, I guess) and bank/credit union/liquor store employees…

I have a sole prop and my DBA is something like: “Sneaky Pete Production Works”. I’ve only ever needed to deposit one check in my business checking account but will be depositing many checks shortly. My question is this: can I have clients write checks simply to ‘Sneaky Pete’ and will I have any trouble with the bank? It’ll be shorter and easier for everyone, not to mention that I market the company simply as ‘Sneaky Pete’.

Just so you know, I don’t want to ask the bank beforehand if I can help it. I have a small business rep there who knows me and is super anal about paperwork/dotting every ‘I’/crossing ever ‘T’. I don’t want to get redflagged for this if it won’t be an issue. Then again, I don’t want to end up with a check I can’t deposit.

Also, when I have more cash, I might change my DBA but that’s not much of an option currently.

Thanks!