Perhaps it is wisdom to use both the names for about a year because the old domain name will bring prospective clients to you which you can easily convert into a proper sales. It is important to be visible and then wait for the invitation.

As per my personal experience I had www.angloindia.co.uk the name established with my clients but our partnership changed and we wanted to do business with a new domain name www.ProfitMentoring.com

When somebody clicked on www.angloindia.co.uk then the site automatically got transferred to www.ProfitMentoring.com and this way we got the maximum benefit of our old established name as well