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 > Web Chat section > </> 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: https://developers.freshchat.com/#customisation-wgt