Huawei Technologies’ long, deliberate attempt to shift its image from a copycat to an innovation leader suffered a recent setback, not by flubbing an important technology but with the design of a new campus for the Chinese telecommunications giant.

Photos of architectural renderings and videos of the new headquarters for Huawei’s smartphone division outside the southern tech hub of Shenzhen came in for a critical drubbing when they cropped up on websites and social media last weekend. Attention focused on images of the lakeside...