Personality trait in which the person's style is evident in all they do?

Solution 1:

hallmark (noun):

a typical characteristic or feature of a person or thing

'Simplicity is a hallmark of this design.'

Source: CDO

signature (noun):

a distinctive mark, characteristic, etc, that identifies a person or thing (3a)

Source: Collins

Solution 2:

For a comprehensive list of personality traits see

http://www.emotionalcompetency.com/adjectives.htm

A trait that indicates a person's style is stamped into everything they do is consistent:

consistent

adjective

(Of a person, behavior, or process) unchanging in achievement or effect over a period of time: manufacturing processes require a consistent approach
_ODO

Another possibility (though not on that list)

congruent

adjective

In agreement or harmony
_ODO