I see no reason to worry.
If you are concerned, do a test - create a new WS/LP pair, create a smart list that references them, then edit the names. Check the smart list to see if change occurred.
Only tokens do not auto update across assets.
You may want to check in with support that you are doing this.
Once you do this, double check key campaigns that reference the Partitions and WS to ensure the names took. Do it one by one to see the effects.
Thanks for your response . I got some more information from our technical support representative and it turns out that we are using the custom integration "Sync Leads" and will need to coordinate with our technical team to ensure that we don't break the integration by editing the workspace and partition names.
Do you know if there is a step-by-step process that I can refer to for how to make changes for this type of integration?
Nope. I'd have to be in your system. Whoever built or owns that custom sync needs to help you.