In my imagination the additional code in the blockchain looks just like "1561BfPq4HAp8BpE3rDoojyqCgbo3BTvdb=TheOnly1" 
But I fear it is not that easy...
So you still need an address? What's the point then But I fear it is not that easy...
As I am not a programmer, I think the addresses are still needed for the system. But in my oppinion users should not be confronted with addresses and stuff. Just with theyr choosen wallet names.
So nothing else is needed than a possibility to connect a wallet public key with a name. I dont think this is such a difficult and big change in Bitcoin system...
Get it??
If the address is still needed then you have done nothing, because you will still need to get it from somewhere, be it a qr code or another service. It actually is difficult to add this to bitcoin directly, that's why it should be added as another layer on top of it (offload it to wallets directly) using a different blockchain.