It's not to complicated unless something else is stopping it, but;
1) Select the cells you'd like the conditional formatting applied to
2) Click 'Conditional Formatting' on the menu
3) Select 'Highlight Cell Rules'
4) Select 'Equal To'
5) Select (or type) the Cell with your drop down list.
And that should be it really...
You might be running into something wrong with your data, for example if your list of names you want highlighting has some trailing spaces. You can check for this by clicking into the cell and seeing where the cursor starts to flash, if it's a couple of spaces after the end of the name then thats why they are not matching; "Sam " won't match "Sam"
... If that makes sense?