You actually need to have the same plane AND livery for it to show correctly in yours.
In multiplayer groups, always use a base livery that comes with a aircraft.
If you do not then it will select the Bonanza (for any piston aircraft), pointy nose A330 (for any jet), and that’s all the AI models I can recall seeing.
Certainly a failing of the sim, that it won’t fallback to a standard livery if you don’t have that, but have a model installed.
If developers could add a streamable low-LOD model that could be streamed to all players within say 50nm, then at least everyone could see the correct model.