"To abbreviate the name" means to shorten or condense the name by using only a few letters or a shortened version of the original name. Full definition
Don't abbreviate the name of the college or university you received your degree from. (livecareer.com)
Enter abbreviated names for your the credit card or lending institution, the current balances, and the interest rate information for all of your current debts (including home equity lines of credit or second mortgages). (vertex42.com)
By abbreviating the names, we emphasise the personal approach of Magnusson, who is just Emma to most of her clients. (creativeboom.com)