That depends on what your optimality criteria are. Mine is to maximize education about modern physics, in which case it is probably close to optimal to explain that the modern scientific community uses the unqualified word "mass" to refer to "invariant mass" and then using it consistently.In general you are right but in a discussion about relativistic mass the unqualified word "mass" is not an optimal choice.
This is an odd response given your previous comments in this thread. You seem to recognize that the important part of the name is the agreement of practicing physicists, but at the same time resist what practicing physicists have agreed on.Could we? The majority of physicists would need to agree with the new name. That's very unlikely.