When I starting receiving injected insulin in 1966, this was the syringe I used. I can't show you the thick needles (25 gauge) and measured 5/8 inches long. They were reusable. Unfortunately my parents were not taught to sharpen them. We just used them until they were mostly unbearable to use any more: around 3 weeks.
Today's insulin syringe needles are much thinner and considerably shorter. But how short is short enough? Put another way: how long is "long enough"?
Read this recent report from The Forum for Injection Technique and Therapy: Expert Recommendations (FITTER) workshop in 2015. It contains lots of great information to update our knowledge of injection and infusion of insulin. It's all about minimizing the risk of tissue buildup, better known as lipohypertrophy.
It's a good read. It's also broken down into sections.
Answer to the above question? 4 mm regardless of age, ethnicity or BMI (size).