Having due diligence as part of your organisation's procurement procedures, where you can then have a list of 'approved' apps and programs helps to prevent fraud, data breaches and identity theft. If staff are unable to sign up/download apps other than through an IT centrally controlled program then the risk is much lower.
When the fake app is a Password Manager app, then the risk is very high as hackers will likely have all of your passwords to your legitimate apps. Malwarebytes Labs has recently reported that Password Manager LastPass has warned about a fraudulent app called 'LassPass Password manager' which it found on the Apple App Store. The app closely mimics the branding and appearance of LastPass, right down to the interface. So, even if the name was a “happy accident” it seems clear that this was a purposeful attempt to trick users installing the fake app. The full report:Warning from LastPass as fake app found on Apple App Store.
Fake apps represent a significant threat to your digital security and privacy, having best practice around downloads in an organisation can help reduce the risk.