I think for most Japanese people Li Bai (pronounced as ri haku in Japanese) is just a name as well. So I think few people would understand that Tōsei was a reference to Li Bai. To most people it was just a silly, perhaps self-depreciating name, the kind that haiku poets often picked.
I think Issa was playfully poking at himself, as usual. Another year of good health, and another with his head lice. His lice were making the life journey with him as constant companions.
Thanks for reading!
!PIZZA