Atlassian accounts don't have any functions for automatically changing a profile's name, there is a human doing it (if it is changing)
Two possibilities though
You are using the account in a system where the name has been cached, either on the service side or possibly by your browser too. If it's server-side, waiting a short time and refreshing should fix it. If it's client-side, try closing the browser after clearing the cache and restarting it.
Your account is owned by an organisation and they are insisting on putting your second name in.
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