Most persons with the name spell it "Courtney' whether male (e.g. Courtney B. Vance) or female (e.g. Courtney Cox).
Less frequently used are "Courteney" or "Courtenay", variations of the original Norman spelling.
Courtney, Courtnee, Courtni, Courtnie, Kourtney, Kourtnee, Kourtni, Kourtnie, Courtny, Kourtny. But more can be added I guess. On my list there's 10.
コートニーKōtonī
It is usually spelled COURTNEY. That's how most people spell it. But I have also seen it spelled KORTNEY and KORTNI.
Your spelling is correct.
another is the correct spelling