You could make use of agent: {hideName: false} as part of the config to hide both the Agent and Bot Name. 

If you're using a Freshsales Suite account, then you can find the above mentioned code under Admin Settings > Channels > Chat Settings > Web Chat Settings </> Embed button.

If you're using a Freshchat Account, then you can find it under Admin settings > Channels > Web widget and access it by clicking on the </>Embed button. 

You can set it to true to hide the agent's name. This would be replaced by the App Name you had configured under Admin Settings Chat Widget Settings > Name and Domain.

For widget customisations check our developers portal here: