Author!Anon here: Hi! To answer your question; they're endearments. Chewbacca is over two hundred years old, and given their backstory (I'm following the original Legends canon for this) I've felt like he's always sort of seen Han as this belligerent teenager who can't look after himself - "Young One" is basically an affectionate older brother term, and might also become a source of teasing a few years down the road.
"Hahnko" comes from a 'zine fic I read ages ago - I headcanoned it as the diminutive of Han's name translated to Shryiiwook, and it's just something that Chewie uses interchangeably as a pet name.
Hope that explains things! Thanks so much for reading!