Step 1: Get Materials
You will need hardwood of your preference - about 12" x 6" x 3/4" (depends on how many letters are in the name) for the main piece that will have the name, and some for the trim around the name; roughly 1/4" x 1/2" pieces. (You could get a 2" piece and rip it down to several pieces) Lastly you will need a 1/4 piece of veneer plywood / hardwood for the pieces to sit on.
Step 2: Drawing the Name
Take your piece of hardwood and draw the name you want. Once that is done, draw random lines throughout the whole piece. Keep in mind when drawing lines, that you need to be able to cut these out, so don't make the lines too close to each other.
Step 3: Cutting Out the Pieces
Next is to cut out all the pieces. Take your jigsaw/scrollsaw and cut out along all of the lines you drew in the previous step.
Step 4: Sanding the Pieces
Now sand all the TOPS of the pieces. Don't sand any of the sides because that will cause gaps to be in between pieces in the finished product. You can also sand any burs off the bottom. Next Sand a 45° angle around each piece. (Or close to a 45°) I Turn my orbital palm sander upside down and sand around each pieces edge at an angle.
Step 5: Crafting the Frame
Take a piece of 1/4" x 1/4" wood and put a miter on one end. Leave it long. Now, put all your puzzle pieces together which will form back into the original size of the lumber you used. Set the mitered piece of 1/4" wood up next to the bottom side of your puzzle. Mark where the puzzle ends. Repeat this for the rest of the frame, being cautious not to move any piece so you can be more exact for the glue up.
Now cut a 1/4" dado 3/16" from the bottom of each piece of the frame. This is where you will slide in the bottom.
Step 6: Putting in the Bottom
Rough cut your piece of 1/4" veneer/solid wood to be 1" too long of the dimensions of your original piece of wood for the puzzle pieces. Take two pieces of your frame and line them up miter-to-miter. Slide in the 1/4" veneer/solid wood in the dado you cut earlier. Now mark the INSIDE of where the dado ends on the miters, so you can get the piece to fit perfectly. Then cut your piece on the marks you made.
Step 7: Glue-Up
Line up the pieces of your 1/4" x 1/4" frame side by side. Put glue on the miters and inside the dado. Slide the Bottom 1/4" piece in the dado and put the frame around the bottom piece. Use clamps to apply pressure evenly. Wipe off any excess glue with a wet rag.
Step 8: Staining the Puzzle
Before staining take a sharpie and write numbers on the bottom of all pieces so that when people take the puzzle out, it will be easier to put together, if they get confused. Next, choose your stain and stain either ONLY the pieces that make the name part of the puzzle; or stain ONLY the pieces surrounding the it. It's up to you what stain you use and what you stain. I've found that staining all the pieces the same doesn't look that great. make sure you let these pieces dry enough because wet stain cant get on the frame portion if you aren't careful.
Step 9: Finishing the Frame
Put a finish on the frame and bottom. I use wipe-on poly because it brings out the grain and I love the look of it. You can also put finish on the puzzle pieces you didn't stain; or just leave them as raw wood. (Preferably put a sealer on them to prevent discoloring over the years)
Step 10: Put It All Together
Sign your name on the bottom piece, or write a note, a To/From, whatever you want! Next place the puzzle pieces in the frame.