The receiver's phone number is not displayed on the DHL label.

Technical background

The phone number will be transmitted to DHL if the following configuration option has been enabled.

You can verify in the log if this actually happens.

However, only the DHL API (webservice) can control which data is displayed on the label. Some information will be processed by DHL but not be shown on the label. This cannot be changed by the Magento extension. A similar problem exists regarding the second street field (address addition), see this article.