Hi Cadeyz, and welcome to the forum!
Absolutely this can be done. I'm not sure how you created your data validation list (just typed the values in the data validation area maybe?) Ideally you should set up a table with the names of the people and their phone number. Then you can use a vlookup formula to pull back the appropriate phone number from your list.
I've attached a workbook that shows this setup.
Hope it helps, and if you have any questions, feel free to ask.