I'm sure I'm not the first one with the idea, but I'd like to potentially pursue this if there was sufficient interest and support from the community.

The idea would be for an alias system which could be used within bitcoin wallets. Instead of having to ask someone for a new BTC address or for their lightning node url, we could instead just ask for their alias. Something like @rebelofbabylon would resolve to my LN node or BTC address.

Taking inspiration from projects like Namecoin, it would ideally be decentralized. Instead of Merged Mining, Blind Merged Mining with the help of SIGHASH_ANYPREVOUT (more info here) would be used as to not create a competing coin. There could be some sort of standard for names (32 character length limit, numbers, letters, some special characters, perhaps rules to avoid "i" and "l" being used in an alias or something like that). I'd also like if it were easy to run this on top of your LN node (which is also a BTC node).

I found this abandoned project which suggests a way to enable privacy with this kind of system. Perhaps instead of storing the association between an alias and a BTC address, the association is with a pubKey and an incrementor state variable is also stored to ensure no address reuse.  

I'm still doing research and gathering ideas. I'm by no means an expert (I realize to seriously undertake such a project, I have a lot of learning to do) and would love any feedback  :-)  

EDIT: I want to add that this sort of system would be optional and in no way would I want to replace BTC address scheme (I couldn't even if I wanted to)