(FORTUNE Magazine) – The image of corporate image makers is probably not as bad as you think. In spite of the catcalls over Allegis (ne United Airlines, later UAL Inc., likely to return to United Airlines Inc.), the name game has never been more popular. According to Anspach Grossman Portugal Inc., a corporate name consultant, a record 919 U.S. companies changed their names in the first half of 1987, up 59% from last year. Mergers and acquisitions accounted for more than half the changes. The search for a new look is spreading abroad. John Diefenbach, chief executive of Landor Associates, a corporate identity consulting firm based in San Francisco, says, ''Our overseas billings have grown 30% annually for the past few years.'' Brian Boylan, managing director of Wolff Olins, a British image maker, claims his firm's fee income has doubled in 18 months. In addition to merger activity, the trend toward privatization is fueling the international boom. Landor designed logos for British Airways before it went public and for several newly public subsidiaries of Italy's Gruppo Ferruzzi. This summer the American image maker unveiled a new personality for National Carriers/Roadline, a recently merged British courier company. The name is now Lynx, suggesting, the company hopes, that service will be faster than before.