The error is explicit: the server name is not correct or is not configured for remote access.
Check your connection string - we can't see it - and use SSMS to try accessing it manually.
Remember that the server name will need to be "complete" - it will need the host domain or IP address for remote access:
Data Source=INSTANCE.DOMAIN.com;Initial Catalog=XXX;Persist Security Info=True;User ID=XXX;Password=XXX
Then check your firewall(s).
If that's all correct, then the DB Admin may have set it as rejecting remote access for security reasons - you will need to talk to them about it.