The author name is being output in the PostView.ascx file from your theme folder. The Category too if it's a category that displays at the bottom of each post.
In the Standard theme, the author is being output in a <span> tag that looks roughly like:
<span class="author"> .............. </span>
If you have that, you would want to remove the entire thing, including the span tags.
Categories looks like this:
<p class="categories"><%=CategoryLinks(" | ") %></p>
Just delete the whole thing.
I'm getting this from that PostView.ascx file, btw. Depending on theme, yours could look different. Feel free to paste your PostView.ascx in here if you're not sure.