Many organizations can't use services hosted within another organization's walls at all. These might be government organizations or organizations dealing with money, such as banking, insurance, and gaming organizations. The causes might be legal or, simply nervousness about letting critical code leave the organization's doors, so to speak.
If you have no such qualms, it is quite reasonable to use a hosted service, such as GitHub or GitLab, that offers private accounts.
Using GitHub or GitLab is, at any rate, a convenient way to get to learn to use Git and explore its possibilities. It is also quite easy to install a GitLab instance on your organization's premises.
Both vendors are easy to evaluate, given that they offer free accounts where you can get to know the services and what they offer. See if you really need all the services or if...