Abbreviating a UUID

The question is whether you want to show part of the UUID or only ensure that unique strings are presented as shorter unique strings. If you want to focus on the latter, which appears to be the goal you are suggesting in your opening paragraph:

(...) While not perfect this shorter version is sufficient to look unique in the context where it is displayed. (...)

you can make use of hashing.

Hashing:

Hashing is the transformation of a string of characters into a usually shorter fixed-length value or key that represents the original string. Hashing is used to index and retrieve items in a database because it is faster to find the item using the shorter hashed key than to find it using the original value.

Hashing is very common and easy to use across many of popular languages; simple approach in Python:

import hashlib
import uuid
encoded_str = uuid.UUID('42e9992a-8324-471d-b7f3-109f6c7df99d').bytes
hash_uuid = hashlib.sha1(encoded_str).hexdigest()
hash_uuid[:10]
'b6e2a1c885'

Expectedly, a small change in string will result in a different string correctly showing uniqueness.

# Second digit is replaced with 3, rest of the string remains untouched 
encoded_str_two = uuid.UUID('43e9992a-8324-471d-b7f3-109f6c7df99d').bytes
hash_uuid_two = hashlib.sha1(encoded_str_two).hexdigest()
hash_uuid_two[:10]
'406ec3f5ae'