EDIT: Sorry if the following is irrelevant, just reread the initial post and found my comment below is not relavent to it. I’m not striking it out in case it could help someone.
I think you can claim anything as your occupation, but if it’s a volunteer or low-paying internship, I would just say I’m an intern somewhere.
I’m in the USA, and was told initially that I should tell Social Security the second I make any money. So whenever you get your pay check, you should go to the nearest office and turn in your paystubs for their information. If you’re in the US. Don’t worry about it being late, you most likely won’t get in trouble. They’ll just adjust things appropriately. I was told that they catch up eventually in any event, but it’s helpful to be punctual with the information.
I talked to a voc specialist, and they said benefits won’t terminate for at least nine months after being ‘gainfully employed’. So from what you’re saying you’re not making that much, so benefits shouldn’t end for you in any event, but they will deduct a dollar for every two dollars you make above a certain amount if I’m remembering correctly (And my info isn’t out of date.). It’s still worth it to have that extra income, in my opinion.