There is one letter in my name spelled incorrectly. The health department said I had to go top the court house to get it fixed... how do I do that?

How do you go to the courthouse? Take the bus, drive, walk?

Normally at this point and time you have to do a name change, and this is done in different courts ( not sure what state, Marion country to me is Illinois?? )
But I would start at the probate court clerk and if they don't do it, they will know what clerk to go to.

What do I need to do in the court in order to get my name correctly spelled

First, please don't start a new thread with a follow-up question. Please use the Answer This Question options.

Second, every courthouse has their own procedures. Why not call the courthouse, or better yet, go down and ask.

There will be a form to fill out, proof of proper current ID, this is just a normal name change, you can change you name to Peter cottontail for all the court will care.

So you go down and change your name to anything you want

There will be a fee and sometimes a court appearance ( but often not)