Names of clients from a previous employer should only be disclosed with the permission of the previous employer. If permission is not required, then clients could be disclosed with discretion i.e. some clients may require their approval before using their name.
Employers want to know by your CV what you did with your time between employments. As to why you left a company could be explained once an interview is gained.
By making a good, well formatted cover letter that has been checked for grammar, spelling and other errors.