You may need to change the Slack account that you post your deployment notifications to. This is essentially a two-step process, whereby you'll need to unlink your old Slack account, then link your new Slack account.
To start, head to Settings -> Linked Services, then click the Unlink button next to your existing Slack connection:
You'll then see that you're no longer connected to any Slack accounts.
To add your new Slack account, click the Sign in with Slack button:
Then, login to your new Slack account and click Continue to approve DeployHQ's connection to that account.
You'll now see your new Slack account in the linked services in place of your old one:
If you need to change any individual project's Slack integration settings, you can do so by following this guide.