When you originally purchased H1Z1, you logged into a Daybreak Games account. That process automatically linked your Steam and Daybreak Games accounts.
Right now you are either logged into the wrong Steam account, or the wrong Daybreak Games account.
We find that almost all players are logged into the wrong Daybreak Games account.
You can locate your other accounts by follow the directions here:
Recover Account
Remember to try all current email addresses you use to retrieve the account you may have linked.
If you still can't find your account and need assistance, try this link:
Need help recovering account
If you have more than one Steam account, try logging into the other one(s) to see if that resolves the issue.
I forgot my Steam account info?
If none of these options helps, you'll need to update the ticket with your SteamID to help us find your account.
How to find your SteamID