How do I manually change my BMI on a forerunner 165?

You can't change only your BMI. It is a formula based on your height and weight. So, height and/or weight would need to be changed.

BMI = weight(kg) / height(m)²

It won't help the poster but you actually can if you have a Garmin Index scale, not that I am recommending getting one but it is possible if you have one or access to one to add to your account.

True, but cannot change the BMI value without height and/or weight being changed. What you can change are the other body metrics, such as body fat % and skeletal muscle mass.

Set Body Composition
If you would like to update the reference values for the body composition metrics measured by your Garmin Index S2 Smart Scale, you can do so using the Set Body Composition setting. We recommend only updating these values using recent measurements from a trusted source, such as a DXA scan or another reputable body composition measurement.

Once you enter new values for these body composition metrics and save your changes, these values will be used as reference points for estimating new metrics each time you weigh yourself with your Garmin Index S2 Smart Scale.