In the podcast "Naming in an AI Age," Ashley Elliott and Mike Carr discuss the importance of social media handles for online branding and discoverability. They explore whether to use separate handles for personal and business brands, emphasizing consistency for recognition while expressing personality. Tips include using timeless language, checking platform restrictions, and conducting trademark searches. They also suggest creative solutions like adding location identifiers or "HQ" to distinguish brands. The key points are maintaining consistency, thorough research, and legal compliance to engage followers and protect intellectual property rights.