Branch, an insurance company, chose Neon Serverless Postgres as their database solution due to its true serverless nature and compatibility with existing systems. They transitioned from Amazon DynamoDB and other providers that couldn't fulfill their needs for complex queries and diverse data access patterns. Neon's scalability, ease of use, and flexibility made it a perfect match for Branch's serverless architecture, leading to significant improvements in operational efficiency, scalability, and cost-effectiveness.