Sure you can use a Sharpie to mark your kids' clothes, books, bags, etc. Or you could use a handcarved custom stamp with their name and likeness.
Kids' pretty much love anything with their name on it. And stamping is fun, too. Make an afternoon stamping onto blank cards for their personal stationery stash. They can mark their books before lending them out to friends. Or use fabric ink on clothing to ensure their clothes come back from daycare or summer camp.
These are handcarved by Etsy seller CraftPudding and can be customized with your child's name and hair color ($20). You can also arrange to have a more specific likeness made from a photograph. In addition to her custom stamps she also carves a variety of really adorable small stamps perfect for crafting. Check out here shop here.