Adapting the process to the team is exactly the spirit of "agile". If you switch to a different word like "lean" then shady consultants and vendor snake-oil salesmen will just come along and corrupt it the same way they did "agile".

In reality there isn't a lot of dogma underlying agile. For example, agile has nothing to do with CSM's, story points, Jira, velocity, "sprints", etc.