My friend and I have the same first name ; the very same ; spelled the same way.
We went to the States for a holiday.
We knew to be on our best behaviour and not upset the nice security people on entry. We were good. She went first. Nice lady inspects her passport, reads her name, lets her enter the country.
She inspects my passport, reads my name. Are you here for a holiday?
Are you two sisters?
Just say no and smile. Not a word more.
Some concern that the final decision about whether or not you get into their country is made by someone who thinks that your mother could have had such a sad lack of imagination.