When you create a label in Gmail, you'll have to supply a name for it: this name will be displayed on the left hand side, to identify said label in the listing, but also be shown inside email messages to which you have applied that particular label (as shown on the screenshot below). Especially since you can add multiple labels to a single email, short names make sense, in which case Gmail lets you can go back and rename a label.
Change the name of an existing email label in Gmail
After you sign in to Gmail, you will be inside your inbox and see on the left hand side a listing of all system labels (Inbox, Buzz, Starred, Chats, Sent Mail, Drafts, All Mail, Spam, and Trash), and all the custom labels you have created yourself.
You cannot rename any of Gmail's system labels of course, but you can change the name of any of the ones you created. The easiest way to rename labels is to do it from the screen you are looking at in your account: locate the label whose name you want to change, if needed by clicking on the "X More" menu if you have more labels than can be displayed at once.
Once you have found the email label you want to rename, click on its color swatch (the square on the left of its name - you will see an arrow when your move your mouse pointer (cursor) above it, indicating that it displayed a menu).
When the label's menu opens, you will see as third command from the bottom a menu item that reads "Rename" - click on it, and Gmail will open a "Rename Label" dialog:
Either edit and adjust the content of the "Please enter a new label name" text field, or select it in its entirety and type over a brand new name for that label.
Click on the "OK" button to apply the new label name: Gmail will update the labels listing on the left, and the "tag" that shows inside all email messages to which that particular label was applied.
This is all it takes to rename a label in your Gmail account; note that behind the scenes, Google doesn't keep track of email labels based on their names, which means that renaming labels will not create any issue: Gmail will simply display the new name instead of the old one, but no email messages will lose the label that was attached to them under its old name.