While creating a new site-to-site tunnel within the new Azure Portal, the name entered for the Local Site, changes automatically to a format where a random number of characters are added to the name entered. For example, if the new Local Site is entered as "Long Beach" Azure will change the name to something like "F5C699CE_Long Beach".
When the deployment for the new Local Site is finished, the name "Long Beach" is not recognized by the PowerShell even though it is listed among the deployed Local Sites on the new Portal. To get the actual name, one has to go back to the old portal, download the configuration file, where the true name is listed as "F5C699CE_Long Beach".
I have to mention that the Virtual Network used in this deployment is a Classic Virtual Network.