"Jug" would, of course, be Gene Ammons. Distinctive player out of the "Texas tenor" tradition. Very assertive style and HUGE sound.
The issue if jazz nicknames is a fascinating one. O-10, there is some truth in what you say and thanks for bringing up the topic which is one of the most fun details of this music. However, I think that as written your comment exaggerates the connection to "arriving" on the jazz scene. What about all the great players who do NOT have a moniker? Does that mean that they have not arrived? There have been many. The danger in generalities I think. In fact, an interesting extension on this is that how a musician is addressed by colleagues sometimes comes around full circle. In other words, sometimes the ultimate sign of respect becomes NOT the use of the always used moniker when addressing the esteemed player, but the use of the formal first name. Example, in "musician speak", a player might have, for instance, referred to "Duke" as Edward (his real name) as the ultimate sign of respect. A subtle and very inside thing. Interesting comments on the topic:
http://blog.oxforddictionaries.com/2015/04/jazz-musicians-nicknames/