Can I put my Copyright name on a photo with my Nikon D50?

I have a Nikon D50 and I want it to automatically put my name on all my photos. Is there any way? Any way to make a logo or a certain text style and upload it to my camera?

No… That requires software. Besides if you could it would look terrible. Best bet is software using what's called a watermark or other small notation about your name and date.

Look on page 70 of your user manual.

There's a feature called User Comment.

There you can put your copyright notice and it will show up on the EXIF data on each photo you take.

Place this notice in the User Comment: (C) 2013, Your Name, Allrghtsreserved). You are limited to a total of thirty-six characters, so you may not get the while "All rights reserved" on the end of your notice.

In the end, if you are shooing in RAW and using Adobe Lightroom, you can add your copyright notice, keywords, contact information and other things to the files metadata

NOTE:

When posting any of your shots on websites or in email, resize those specific images so that they have the longest size no longer than 600 pixels @ 72 PPI and use a watermark right across the middle of the image. REMEMBER to save this modified file as a different name so you so NOT overwrite your original image.

I place an "i" in front of each modifed file to show me that they are internet ready.

Sample: _DRS1234 becomes i_DRS1234

Your camera can put a comment in the EXIF header with your copyright info. They don't have a copyright symbol (it's not part of the standard ASCII extended character set), so you'll need to spell it out, or do what others have done and use "(c)" for the copyright symbol. See page 70 in your manual.

If you want to add a "copyright" meta tag to your EXIF data, use ExifTool to add this info.
The command line to edit all your JPEG images in a directory is:
exiftool -copyright="1990 George Jungle" *.jpg