Dear @Peter Mansell,
Thank you for reaching out to the Microsoft Q&A forum. I am happy to assist you.
Teams usually reopens with the account that was active when you last closed the app, rather than the account you prefer by default. In addition, if you are using both a business account and a personal account in Teams, the app creates a separate Teams profile for the personal account.

I have tested this on my side, and even if I close the business account and only use the personal account, Teams still signs in with the business account when the app is reopened.
At this time, Teams does not offer a built‑in option to select a default account. However, as an alternative, you can pin the preferred Teams profile to the taskbar for quicker and more convenient access.

To pin the preferred Teams profile to the taskbar, follow these steps:
Open Teams and sign in to the profile you want to pin. Then, right‑click that profile’s icon on the taskbar and select Pin to taskbar.

The profile will remain pinned, and you can open it anytime by clicking the pinned icon.
I agree that having an option to set a default account would be very helpful for managing multiple Teams profiles.
So I encourage you to submit feedback directly to Microsoft via the Teams app (Help > Give feedback), or through Feedback Hub by
Go to: Microsoft 365 Feedback Hub > Send Feedback > Describe your proposal in detail.

Sharing your experience through this channel is the most impactful way to advocate for a change that would benefit you and other users.
Thank you again for your patience and for bringing this to our attention. While I can't change the product's design, please don't hesitate to reach out if you have any other questions about its current functionality. Your perspective is important, and I’m confident it will support the continued development of the Teams experience.
I hope this information is helpful. If you need any further assistance, please feel free to reach out. I am here to help. Thank you very much for your understanding and cooperation.