Unexplained messages

In recent months, my phone bill is showing messages to one mobile number that I have not sent. These could occur at any time and even when I did not have the phone with me.

I saw no evidence of these messages on my phone and the recipient is clear they did not receive them, only becoming aware of their existence on my phone bill.

No one else had access to my phone, I have no other Apple device.

There is also evidence of missed facetime calls from the same recipient.

Could anyone give any indication of how this could have occurred please? I am aware of an issue with IOS 12 and the merging of contacts but am unsure of the implications of this.

Thanks for any help anyone could give.