You are not actually asking to apply a signature to a real life object but you are only asking how to create a signature which can be associated with you and with nobody else. What then happens with this signature is another thing: you can attach it to the object you own or you can attach it to an object you don't actually own. Others can remove the signature, copy the signature, put it somewhere else or destroy it. Thus the actual use of such a digital signature in real life is limited.
Still, you can create such a signature if you have a digital identity based in public key cryptography and where the identity is accepted by others. This can for example be a smartcard, a PGP key, an S/MIME certificate etc. All these allow you to sign something and that's actually all you need: for example you can sign a description of the item with it.
But again, real ownership cannot be proven this way. It would be different though if the items you want to mark already have a unique identification, like a serial number you can find in car chassis or bike frames. In this case the act of ownership transfer could be digitally signed, i.e. the vendor digitally signs a contract which transfers ownership to you and if you give the item away you also sign such a contract for ownership transfer. This way nobody can just claim something as its own but must actually prove how they got it by showing the contract. In reality this gets way more complex than that but this is the basic idea.