Agile was defined with this name in the Agile Manifesto, which was born from already existent experience, practices and methods.
Martin Fowler - <<Agile Development is adaptive rather than predictive is people-oriented rather than process-oriented>> [b1]
Comments: Martin Fowler describes here the adaptive core capability and a core aspect people-oriented. Why people-oriented? Having these software development traits: complexity, incertitude & changes, in a context of knowledge work we cannot be lean and adaptive without being people-oriented.
Scott W. Ambler - <<An iterative and incremental (evolutionary) approach to software development which is performed in a highly collaborative manner by self-organizing teams within an effective governance framework with “just enough” ceremony that produce high quality solutions in a cost effective and timely manner that meets the changing needs of its stakeholders>> [b2]
Comments: Scott Ambler definition has synthesized here the logic inside Agile Manifesto with only one phrase. It is all about <What IS Agile> and it is more robust ( ~ solution over working software and stakeholders over customers). From the <How> part of Agile Manifesto is missing only the explicit reference to the good design/technical excellence. That is, probably, the best definition, other than Agile Manifesto.
Alistair Cockburn - <<Agile implies being effective and maneuverable. An agile process is both light and sufficient. The lightness is a means of staying maneuverable. The sufficiency is a matter of staying in the game>>. [b3]
Comments – Described traits: effective, maneuverable, “light and sufficient” and steady. For this domain, to be effective, maneuverable and steady you should be Adaptive while being Lean. Light and sufficient it is kind of description of a lean approach for software development domain problems. “The lightness is a means of staying maneuverable”: lean is mean for staying adaptive. Lightness is only one aspect of being lean.
Remember … from OOPSLA to Snowbird – most of the Agile Manifesto authors have been previously met at OOPSLA conferences, so they are all interested in good design. Martin Fowler has said: “If you are in the Mud, you aren’t going anywhere!”.
[b1] Martin Fowler about Agile
[b2] Scott W. Ambler About Agile