These database waypoints are discussed in the chapter on databases. On most unit they must be no more than 6 characters long and contain no spaces but can contain any combination of letters and numbers and some punctuation.
The newest units permits 10 character names and these can include spaces.
Averaging still can reduce the some of the effect of a temporarily poor DOP.
While averaging is going on you can move to the name field and enter the name you wish so that when you have achieved a stable FOM you want you can save the results.
Garmin receivers have differing capabilities in the number of waypoints that they can save.