The management api doesn’t do link resolution (which means the UI Extension SDK doesn’t either), so it might be useful to instantiate a delivery or preview api client inside your UI Extension simply to get the tree of content more easily.
For example, I built a nested category browser UI extension which displays a tree of categories to reference from another entry and I used a CDA client to get the tree of categories within my UI extension.
You also could iterate through all the entries and for each reference do a space.getEntry(id) to get all the names. Or you could do it in one api call like
space.getEntries({
content_type: 'content_type_id',
// a comma separated string of all the entry ids
'sys.id[in]': '16kHM2yIJOdZbV4TTQ2E5i,4WOwG2lL15gEG62TckFZXW'
}).then(response => {
// get the entry names
})