Both names can be changed from your profile settings.
Display name (30 days)
Your display name is what other people see. You can change it once every 30 days. The cooldown exists so the people who follow you aren't constantly seeing a different name.
Username (90 days)
Your username is your login and the slug of your profile URL (/@yourname). Changing it breaks any external links to your old @handle. The 90-day cooldown reflects the seriousness of that.
Early change requests
If you genuinely need an earlier change — got married, name correction, a vocational shift like becoming a pastor — go to Edit Profile and submit a request. Include a brief reason. An admin will review and approve or reject within a few days.