As an AI language model, my responses are based on the information available up to September 2021. The ranking of fastest-growing companies can vary from year to year as market conditions change. Therefore, it is essential to refer to the most recent financial reports and market analysis. However, I can provide information on some notable fast-growing companies in the S&P 500 as of September 2021:

1. Moderna Inc. (MRNA) – A biotech company known for its COVID-19 vaccine.
2. Tesla Inc. (TSLA) – A leading electric vehicle manufacturer.
3. Etsy Inc. (ETSY) – An e-commerce platform specializing in handmade and vintage goods.
4. NVIDIA Corporation (NVDA) – A technology company focused on graphics processing units (GPUs) and artificial intelligence.
5. PayPal Holdings Inc. (PYPL) – A digital payments platform operating globally.
6. Twitter Inc. (TWTR) – A social media platform that enables users to share and discover content.
7. L Brands Inc. (LB) – A retail company that owns brands such as Victoria’s Secret and Bath & Body Works.
8. Fiverr International Ltd. (FVRR) – An online marketplace connecting freelancers with clients.
9. Square Inc. (SQ) – A financial services company known for its mobile payment solutions.
10. Zoom Video Communications Inc. (ZM) – A video communication platform that gained significant popularity during the COVID-19 pandemic.

These companies have experienced rapid growth in various sectors, benefiting from shifting market trends and technological advancements. However, it’s important to do further research and consider consulting up-to-date financial reports for the most current information.