Can last names be shortened just as first names?
Solution 1:
Shortened versions of surnames (last names) are often used as nicknames in English-speaking countries, but normally by people on very familiar terms with the person and therefore not in quite the same way as Robert might be shortened to Bob or Steven to Steve.
In my experience (predominantly British English) longer surnames such as Robinson and Brightman might be shortened to Robbo or Brighty or even extended from one sylable to two with the addition of an "o" or "y", e.g. Brown to Browny.
I would emphasise that this isn't something that would happen outside relatively close circles of friends, teammates or colleagues.
Solution 2:
Shortened names are also known as nicknames. They're generally casual, shorter versions of a person's first name (Like Andy for Andrew), though they can be assigned based on features or characteristics, as well (Shorty, for example).
A nickname could be taken from a last name; it's feasible that George Macintosh, say, could be called 'Mac' by his friends.
There is no other reason that I can think of in which a last name would be shortened. It is not standard practice and could in fact be quite confusing!
Solution 3:
Only colloquially and among friends. Sometimes the name is lengthened in such circumstances, For example, 'Jones' can become 'Jonesy'.
Solution 4:
Nicknames come into use either because the original name is long and/or cumbersome and the nickname is shorter and/or catchier, or as a term of endearment.