Change display name folder set

When I look at my Outlook folder list I see that the set of folders of my Exchange account is named after me, the one for Live Hotmail holds my email address and a pst-file that I have is named “Personal Folders”.
How can I change all these?

While they all show in your Folder List, they indeed are managed differently when it comes to naming them.

Exchange
Exchange mailboxes are named after your display name as your (corporate) administrator has configured it. In front of it is the word “Mailbox” so it will look like; “Mailbox – Display Name”.
There is no way to remove the Mailbox part. If the display name gets changed on the server (for instance when you get married), this won’t reflect to Outlook unless your mail profile gets recreated.

Personal Folders, Archive, pst-file, IMAP accounts
The display name of these folder sets can be renamed quite easily;
Right click the root of the folder set and choose Properties-> button Advanced…-> tab Advanced…-> field: Name

Live Hotmail
Live Hotmail accounts are always named after your email address. The Outlook Connector doesn’t have any option to change this. If you want to change it, you can use a free tool called Live Hotmail Rename Tool. This also allows you to rename the account name itself from your email address to a display name you like better.