To save a Component…
Use the component context menu command Save As, which creates a new SKP file.
To Claim Credit as Component Author…
Go to the folder where you saved that new SKP component file.
Double-click on the file to open it in SketchUp.
Notice in the Model Info - Credits panel that the Claim Credit button is grayed out.
What to do?
Here’s the trick…
Take the Line tool and draw a line somewhere in empty space away from the model.
Now notice in the Model Info - Credits panel that the Claim Credit button is active.
Then … Claim Credit > Erase the Line > File Save > File Exit
Now when you import the component into a new model file you’ll see yourself in the Component Authors list.
You’ll find the Claim Credit method described above in Scene 9 of this SketchUp tutorial model.
Saving DCs and Uploading Them to 3D Warehouse — Tutorial Model by SketchUp
This SketchUp Help article describes the Claim Credit method in detail.
Using the Credits Feature — SketchUp Help