Do large language models (LLMs) possess a measurable "personality," and how do the linguistic properties of training corpora shape their cognitive style and downstream reasoning? This paper approaches these questions from a sociolinguistic perspective on machine "identity." This manuscript is positioned explicitly as a conceptual perspective paper: it does not present original experimental data, nor does it constitute a systematic review with defined search strategies or inclusion criteria. Instead, it synthesises key published findings into two original theoretical frameworks intended to guide future empirical and engineering work. We examine evidence that LLMs exhibit reliable, valid Big Five personality traits—particularly in large, instruction-tuned models—and that continued pre-training on domain-specific corpora may shape those traits through measurable linguistic features: imperative ratio, type-token ratio (TTR), and syntactic complexity. We then analyse how standard-language ideology embedded in training corpora is amplified in model outputs, disadvantaging dialect and minority-language communities. Building on these findings, we propose two conceptual contributions: (1) a Personality Engineering (PE) framework for targeted continued pre-training to cultivate task-appropriate cognitive profiles, and (2) a Language Ideology Propagation Model (LIPM) mapping the pipeline from corpus composition to societal impact. Both frameworks are explicitly conceptual and require empirical validation before they can function as operational guidelines. Their value lies in structuring future research and providing a shared vocabulary for cross-disciplinary collaboration, with direct implications for responsible AI deployment.