Name will essentially be the text after the c/ in the URL
Display Name allows extra text and will show when people browse using the Communities tab. Text in the Display Name is also searchable
example: I made a community called 'retronet'
that is the Name, which corresponds to this url: https://lemmy.sdf.org/c/retronet
the Display Name is 'retroNET - Vintage Culture/Websites/Software', which is what people see in the Community browser