Can't replace the selected cell address with the content name.

I have a list of records showing the names and some particulars of the people.
When a person has left, I need to delete him/her from the records.
I have one method (Method A) which allows me to select a data (say name of the person) and then using vba to delete the entire record.
But instead of the name of the person appearing in the input, the cell address is shown instead. I can't find a way to replace it with the name of the person selected.
So I would like to have a drop down list of the names of the persons in the records
where I can select and then clicking on a "Delete" button (using macro) to delete the data of that person from the reocrds.
How can that be done using vba?
I'm using MS Office 365 Excel. I've attached a sample file here.
Thanks in advance.
KSChan

Thank you, Alansidman for your quick solution.
I've tried your VBA code and it works perfectly.
I've added two more command lines: One to sort the names after a deletion and second one to re-number the Record No.
Now I can abandon Method A as it looks very odd to have the cell address showing instead of the name of the person.
Thanks once again for your help.
Chan