If you are just trying changing your current Apple ID name because it is not an @mac.com, @me.com, or @icloud.com email address, you should be able to do so by going to
My Apple ID and choosing Manage your Apple ID. You can only do this (despite what the site seems to imply) if your current Apple ID is not an Apple email address.
Otherwise:
All your Apple purchased content (including the apps) are associated with your Apple ID. If you want to keep those apps, you'll have to keep the old ID.
You can have more than one Apple ID, and use them on the iPad. It just means you have to keep track of what was bought using each ID, since you'll have to log into the various iStores with the same ID in order to update or re-download content. Some people do this to get apps and contend that are not available in their regional iTunes Store.
Now, to address your question.
If you delete an app it will delete the app's contents and files. Any attempt to restore a backup from one Apple ID to another might work, and it might not. I've not experience with this. What I will say is you should not rely on getting your important files from a backup, even if it is supposed to work. Backups are the last resort, for when you get caught unprepared.
Since you know what you are about to do (or not) you don't have to rely on the backup for Pages, and most other apps' documents. Instead, save the files to a computer or cloud service (not iCloud in this case, since it is probably associated with your current ID).
The methods t accomplish this will vary with the app. If you only have a few files of modest size, you can simply email them to yourself and save them on a computer. Some apps offer DropBox, Box.co, or other cloud service support. Pages will save to Box.com using the WebDAV option.
Things like Contacts, Calendars, etc will require some method of importing and exporting. Some of this can be doen from icloud.com on a computer. Other's may require a visit to the App Store.
Your place in Games and such are probably going to be lost, unless restoring from the backup works; and even then not all games save their progress in backups.
In short; you can change your Apple ID if you prepare throughly, and are willing to either keep both Apple ID's for purchased apps/content or take a hit buying your old stuff back.
