I have CS5 with a private account, and CS6 and CC from the company I work for (I need all this because I have students with different versions).
I installed just now CC 2014, and I see I got a trial, based on my private account.
Is there a way of changing this without uninstalling?
Yes you can change the account without uninstalling the program. Please follow the article: Sign out, Sign in | Creative Cloud Desktop app and sign in with your company's account.
Let me know for further query,
I shall do so in 1 or 2 days (am away now) and shall let y know.
Worked fine, thanks.