Yes. The dedicated bot add-on ($7/month, on Pro) runs OnyxBot under a bot you own: your name, your avatar, your presence in the member list. See what Pro costs.
What it is
Instead of the shared OnyxBot bot, your server gets its own dedicated instance signed in with your bot's token. Members see your brand everywhere: on panels, in tickets, on AI answers.
What you need
A Discord application you create in the Discord developer portal (five minutes, free). You provide its token in the dashboard and OnyxBot handles the rest, including keeping your instance online.
What changes functionally
Nothing. Same features, same dashboard, same knowledge. It is purely identity, plus the isolation of running as your own instance.