I recently came across this sentence:
However, one headquarters sounds odd to me. Is this correct?
Although it may sound odd, one headquarters is grammatically correct since it is a count noun and can be modified by any number, including one.
Try rephrasing your sentence to make it sound more natural. For example,
OR
. . . six regions and their (national) headquarters.
OR
. . . six regions and its (national) headquarters.
OR
. . . a headquarters and six regions.