What does the .obj file contain?
If the file is from a surface scanner and you want to display texture then you can follow these instructions: Displaying textured 3D models
If exported segmentation to .obj and trying to load that then you can restore the original segment colors but it requires manual steps, as .obj is primarily used as an export format in Slicer. When you read a .obj file then object IDs are stored in the model nodes as scalars. You can use these scalars to set different color for each segment (Models module / Scalars section). If you use the colormap of the original segmentation then you’ll get back those colors.