Does this ever happen to anyone? They become like someone else with their personality with others?

So with BPD (and attachment disorder, and more) I have been severely neglected and abandoned young in life by my mother. I didn't develop an identity, so I copy others.
In weakness without thinking I copy my mother's personality when I'm angry with some people. Usually the frustrating ones. I talk like her and use her words, expression, and tone.
Then I am sick with myself. I hate that person!!! (when I'm not loving her).

I wish I had developed my own strong personality, normal relationship to others and know my place, and the ability to be loved without wondering what's wrong with the person loving me until I push them and everyone away. It's not something to brag about.

At my age this is getting old!