Voicings
A voicing is the specific arrangement of notes in a chord stack.
An E- chord might be voiced as:
E G B
E B G
B G E
E G
E B
E G B G
E G B D
E G D Fs
Fs G B D
E G B
E B G
B G E
E G
E B
E G B G
E G B D
E G D F
F
Yup! You don't always have to use notes exclusive to the triad - not even the root.
Triads are tools to build arithmetic, they are not necessary musical implementations.
Of course, dense harmonies and rootless voicings might not always be the best choice.
That choice depends the on context of the music being played.
However, neither are chord symbols obligations that E- means you must always play E G B.
There is no right or wrong. All answers are correct; in the correct context.
The only 'rule' in music is: Does it sound good?