How to change where the mii is from on Nintendo 3DS

Hopefully, this describes what you want to do. From Nintendo:

How to Change the Mii Character Used in StreetPass Mii Plaza

Important Note! Only a Mii character that was created by the user can be used as the display Mii.

What to do:

Select StreetPass Mii Plaza on the HOME Menu, and tap "Open."

Highlight your Mii Character and press the A Button.

Select "Mii Settings."

Select "StreetPass Setting."

Select "OK."

Choose Mii from the list of Mii Characters. Select "Yes" to confirm.

Note: This is the only Mii you can change - you can edit your personal Mii, but you cannot delete it or switch it for a different Mii you have created. (It actually warns you about this when you create them, and also in the manual.) Also, if you attempt to delete them, you get a message that says "Your Personal Mii cannot be erased." You can re-format the 3DS, however, in order to create, effectively, a blank slate for yourself, but editing the Mii is really your only option if you do not wish to take that route.

If you want to reformat the 3DS, go to System Settings -> Other Settings -> Format System Memory (it is the last option on the 4th page.) The following information will be lost after formatting the system memory:

• All data in the System Memory (including Friend List, Notifications, and step count)
• System Settings data
• Built-in software save data
• All photos in the System Memory
• All other extra data (created by some games and applications)

It will not, however, delete your e-shop account.

I don't know if this is the specific problem you're having, but there's apparently some hardware weirdness when the 3DS is in sleep mode, possibly related to sleep mode with DS games. Exposure to magnetic fields might be part of the problem. For instance, putting a 3DS on top of a DS Lite (which has magnets in the speakers in the lid) can sometimes cause this issue: