There is another person's name showing on my sister's caller ID when I call her from my cell phone. How could this happen?

I called my sister from my iphone, she told me another person's name is showing with my phone number when I call her from my iphone.

How can I get this name from showing on my iphone when I call someone?

This just started happening when I got my iphone; it never happened with any other cell phone I had.

I then called another person and asked them what was showing on their caller ID and they told me the same thing,

"another person's name is showing with my phone number on their caller ID."