There seems to be a remarkable consensus of opinion: "I don't call myself one, I just do them".
Put the question the other way round:
Who is a triathlete?
1) Chrissie Wellington (Pro - Done a few Ironmen with some success)
2) Alastair Brownlee (Amateur world champ - never done an Iron Man)
3) Hussler - GB team, trains full time with a very supportive employer
3) jonathan.e (been competing every season for the last 400 years, won some, lost some)
4) Conehead (Wrote the book, done a few every season for the last three/four years)
5) Jules (done a couple of seasons, no Ironman [I think])
6) Me - Just done one tri, an easy pool based affair
7) My Dog (never done one - swimming and running are coming on, but he'll never master the bike).
If we all claimed to be Triathletes, who would you call a liar?
[Apologies if I have misrepresented anyone's achievements...]