Composer automatically transposes chord names in these two circumstances:

1.When you transpose the pitch of the entire song or some range of measures in the song, Composer automatically transposes the chord names to the new song key for the selected song or range of measures.

2.For an instrument part which has a transposed instrument key, Composer automatically transposes the chord names for all of the measures for that part.    This is done if, and only if: (a) the part displays only one staff, or (b) the multiple staves in the part all share the same instrument key transposition.
 
The transpositions of chord name keys is automatic.  This is generally good.  However, in rare cases where the spelling of a chord name is ambiguous, such as F#7 versus Gb7, and Composer makes a choice opposite of the one you would choose, Composer you can change the enharmonic spelling of the chord name.

Please note that if you change the notes in a chord, Composer will not automatically change the chord name.  However,  you can re-transcribe the chord names for any range of measures at any time, or manually edit the chord name.