Open an add-on program on your computer (Corel Animation Shop, Adobe ImageReady) and create a new animation by going to "File," "New" and "New Animation." Make sure the background is transparent, and size it according to how you would like it to look once added to your picture.
Select the "Type" tool in the tools panel at the top of your screen in the program, which has an "A" for its icon. Experiment with the font, font color and size, then type a name, word or phrase you would like to add to your image.
Go to "Effects" and select "Add Image Effect." You will then see a variety of choices of animation effects. Choose one that is to your liking that gives your text a blinking effect.
Right-click on your text and choose "Frame Properties." Click on the "Looping" tab and make sure that "Repeat the animation indefinitely" is selected.
Save your animation by going to "File" and then "Save As." The default file extension is gif, which is what you want to save your animation as.
Go back to your original image on which you want to add the blinking text and add a new frame to it.
Add your blinking text to the new frame you created for your image.
Right-click on the image and set the frame properties to a number you want.
Save the new image by going to "File" and "Save As" and save as a new gif file.