About a month ago, I made my own logo in (3d) wood. It kinda looked like this:
To make your own logo in MDF or other wood, you will need:
A printer w/paper
Scissors
MDF (1,8 mm) or other wood of choice
A Pencil
A jigsaw
A drill
A file
Sandpaper #80-150
Wood glue
A brush
A can of spray paint
Ok. Once you’ve got all this, we’re going to start.
1. Choose your font, write your logo in word (Choose fontsize +/- 400, about 1 character per page) and print them.
2. Trace the characters one by one on the wood(I’ve chosen MDF because it’s easy to work with.) with a pencil.
3. Now it’s time to cut out the characters with the jigsaw. It requires some expierence, but after cutting out some characters it will be getting easy. 
4. After you’ve cut out your whole logo, file/sandpaper all the corners and the all the surfaces, to make it look better and to make the paint paste better.
5. To make the painting easier, you’ll have to apply a mix of wood-glue and water. Apply this on all the surfaces. If you won’t you will have to paint atleast twice. After you’ve done this, it’s time to paint.
6. Try to spray the sides first, then the top surfaces.
And you’re done!