Hello Lynn,
Thank you for posting your question on Microsoft Q&A forum
To answer your question:
Yes, when you switch to your personal Microsoft 365 subscription on your laptop, you need to remove the apps installed under the company plan first.
Running multiple Microsoft 365 versions on the same device can cause conflict. After uninstalling the organization’s apps, you can install Office apps that tied to your personal plan. Your existing Word, Excel, and PowerPoint documents will remain intact because files are stored independently from the applications.
Feel free reply back to this post if you have any more question, I'll be happy to help you answer them.