Currently only Intercom, Salesforce and Microsoft Dynamics integrations support customer data update option.
Following customer data can and will be updated:
Customer first and last names
Customer company name
If any of the data listed above has been changed other services, then it will be updated with the next customer sync.
Customer data can be updated automatically if you enable the autosync option in the integration's page. The autosync runs once every 24h.
You can also update customer data manually. All you have to do is access the integration's page and click on the Sync Now button next to the list you want to update.