Is phentermine addictive?

Possibly. Phentermine is a stimulant medications to help with appetite, it can alter mood, and for some people that could be addicting. Signs that it is being abused would be taking more than prescribed, using it for unintented purposes, causing impairment with relationships, work etc. Some people may be on Phentermine for a relitively long period of time for obesity, that alone may not be addiction.
Yes. Addiction to diet pills such as Phentermine is often the result of its common ingredients, including caffeine, Ephedrine (ephedrine sulfate) and phenylpropranolamine. These very addictive ingredients make Phentermine an easy target for tolerance, addiction and then abuse. As such medications continue to be easy to access and deemed harmless, they become an even greater risk.