Household size is not limited to the dependants claimed on tax returns. However, if you have a larger household size than indicated on your tax return, be prepared for possible scrutiny. How much scrutiny will depend on the overall circumstances and whether the difference in household size will actually make a difference in the outcome.
If you will have means test issues, it is best to hire an attorney to handle your case and navigate the landmines of the bankruptcy path.
There is no set definition in the Code. The easiest proof is what is on tax returns. But if you have a legit argument that you have more dependents than that, you can probably claim them depending on their situation. That being said, the Trustee will typically object to claiming adult children as dependents.
The information provided in this post is not "legal advice." Rather it is general information on common legal issues. If you have questions concerning your specific situation, it is always best to consult an attorney in your area.
They do not have to be on the tax return. If they act like a household, they are generally part of the household. I have heard of a case in which the household was a woman, her husband and kids, and her ex-husband, who also lived there. The answer as to who is in a household is more fact intensive than looking at any one document.