Hi, I came here with an h2b visa 2 years ago, and now my status is illegal. I just got married. I want to take my husband name but I don't know what do I have to do. At the court, they told us that I need to go at DMV and at social security. I live in Florida, and my ID is from a different state.
Can I change my name now, or do I have to wait till my status changes?

It depends on which agency. Some will require evidence that you are in status, others will only want to see your marriage license and other identification.

What agency?

Each agency is different, you will need to call them or apply directly. If they don't approve the name change, generally they will only deny it, nothing more.