Inceldom is a condition. Men who want to but can't get laid are incels.
But when people hear about incels they think about the things that are associated with the condition of being incel.
For example, incels are likely to create communities and discuss blackpill-related topics. By doing that they are also forming a subculture (memes, words, categories, catchphrases, etc), so they are now part of their own bubble. This is what society sees as "personality".
Because incels can have lots of personalities. Some are edgy, some are really chill, some are repulsive, some are nice. But the things that make incels a community is what society sees as "personality". So they lump us into one personality based on the things we say online like we aren't any different from each other.