It was called vrtk.unity.core but now it's called zinnia?
Is this a new product or is it just a simple name change from the previous repository?
Do I need to download it again or is it ok to keep the existing repo I have cloned?
Zinnia is just the new name for the previous VRTK.Unity.Core repo so it is just a simple product name change.
The previous cloned repos will still work because GitHub will automatically redirect any of the old URLs to the new URL.