To start chatting with users over Slack all you need is a Slack account. Once set up, your worspace users will be able to message you over Slack and you too can respond them back.
Requirement to implement Slack Chat
How can I start conversation directly on Slack?
To get your users as Slack Contacts, they’ll have to message to app or in the workspace first.
What is Slack messaging window
Messaging on Slack is relatively straightforward. Although other messaging app business accounts place limits when you can message and what you can send, Slack doesn’t place any such limitations on brands.
Since Slack doesn’t have a messaging window like other messaging apps, you can message in workspaces any time after they become a contact.
Its not possible to change App name, however messages display name can be customised.