I just graduated from my university, and I have a paper to submit to a conference. I was filling out the information to submit my work to them, but I am not sure what to put as my organization. Since I have now graduated from the university, can I still use their name to publish my work? If the answer is no, is there any solution to get my work published?
The affiliation to your name on a publication should reflect where most of the work was done and where most of the funding came from.
Scenario 1 You just graduated and you want to publish your results in a paper. The manuscript will be written after graduation, but essentially all the results come from pre-graduation work. The affiliation is clearly the university where you graduated.
Scenario 2 You just graduated and continue researching on the topic. The new paper is an extension of your previous work, but all the work has been done by you after graduation. The affiliation is clearly not the university where you graduated. All the previous work should be cited accordingly. You can submit a paper independently, but it will be easier with a university affiliation. Talk to your former supervisor for advice.
Scenario 3 (in between 1 and 2) You just graduated and you did some new research after graduation. However, a non-neglible part of the manuscript is from before graduation. In this case, you should talk to your former supervisor and ask for their opinion. In my opinion, they will be more than happy to have the paper submitted under their affiliation.
This answer is an extension of what Vladimir F said in the comments.
To broaden the answer a little. I am not aware of any university that requires approval prior to publication, but some organizations (e.g., US government labs) have policies regarding what work can be published and the steps the authors need to take regarding dissemination of the work. If your prior university/organization had such a policy, you should still follow them.
The affiliation can be the one that you are currently with (eg a company/new university), or the old one if you’re still looking around for a job. What’s important is that a. You offer an email address that will be active for a reasonable amount of time. b. That you mention that most of the work was done when you were in your former university.
Both choices here could prove to be seriously wrong. If you use the affiliation, you could be seen as misrepresenting yourself and the institution. If you don't use it, you could be seen as failing to give credit where it is due (especially if you received funding or other support to perform the work that you are now publishing). So, the only correct course of action is to ask your former supervisor (or other appropriate contact) at the university, what you should do.
One option would be to get a visitor or guest affiliation with your old university. These are usually easy to get, and my experience has been you just need to fill a form out with basic contact details. This let's you still put your old University as your affliaition. Usually you will also get to keep your old email address for another year which can be helpful as people don't always update their address books straight away.