You need to get the
Name column from
Buildings and extract the matching record by index number:
This is standard R subsetting of data frames, nothing specially spatial here, and should be covered in any good R introduction, where you'll learn all sorts of other tricks for working with data frames.
You could even do it in two steps if you might want to use the matching row again:
nearest_311 = st_nearest_feature(my311, Buildings)
name_of_nearest = Buildings$Name[nearest_311]
311 is probably not a good name to give your data, so I've called it
my311. Have you really called it
311? Because it helps if your questions use real data names and examples.