Is it possible to put my logo or the name of my site in the blender theme (in the header)?
Just for fun.
The logo is in the Icon File, so you can edit that.
As for your website, you’ll have to go into the source for that.
But are you allowed to do that? Don’t you have to give attribution to the makers of Blender (i.e. the Blender Foundation).
O no I don’t want to change the blender logo in blender or change that but I want to add the name of my site or a logo in the header of blender.
Right now I am walking in a blender t-shirt.
Well I’ll look for you to see where you might change it. Might take a bit… 
Okay, I found where the text is specified:
lines 216-219 in blender.c (blender/source/blender/blenkernel/intern).
Change
sprintf(versionstr, "www.blender.org %d", G.version);
to
sprintf(versionstr, "www.yoursitehere.org");
Leave inthe %d and G.version if you want to keep the version number there. Also make sure your text is less than 48 characters long, or you will overfill an array. If it is necessary to have it longer, you ought to be able to change the declaration of versionstr to something larger.
You ought to be able to display your string so long as you keep it about the same size. If you want to try to make the little colored bar bigger (so that you can include more text), it looks like you can do that at lines 2232-2239 header_info.c (blender/source/blender/src), but I’m not sure how to do it.
Hopefully you already know how to compile so that you can make these changes and use them.
Now I applaud myself for being able to find these things. Blender’s source is very confusing, and I only started to learn C on Saturday (skipping Sunday to learn how to use Vi).