There are a few possible reasons why profile icons in the sidebar messenger might not be showing names:
The messenger is not loading properly. Try refreshing the page or opening the messenger in a different browser.
The messenger is having a glitch. If the problem persists, report it to the messenger's developers.
The names of the people in your sidebar messenger have been turned off. To check this, go to the messenger's settings and make sure that the option to show names is enabled.
The people in your sidebar messenger have not set their profile names. To see their names, you may need to ask them to set them in their profile settings.