I named mine Leo taking it from iLEOstomy. The reason for naming is because I have four children ranging from 13 down to 4. It is a lot easier for them when we discussed my disease to say Leo instead of ileostomy or stoma. Also making it more of a person helps with my children understand it as saving my life instead of just being some sort of disabling surgical solution. By doing this they seem to really accept it for what it is instead of looking at me like I am some sort of poor disabled old man.
Naming your ostomy seems to be a form of acceptance of having it.
John