WASHINGTON—The U.S. Navy once again will let enlisted sailors use traditional job rating titles, according to an official announcement Wednesday, an about-face by top leaders who wanted to scrap a system as old as the Navy itself but who faced pushback from sailors world-wide.

Traditionally, an enlisted sailor’s title has consisted of both an occupational rating and a pay rate—for instance, Electrician’s Mate First Class or Culinary Specialist First Class. In September, Navy officials announced a new system that would give...