I would like to share my method too.
It depends on how many names you have in your layer. If not so much, then this is for you.
First, make a model like this
The empty figure called name is a variable string parameter.
The expression of tool Select Layer by attribute make a selection based on what word will be in Name parameter.
After you made a model save it and open its properties.
Here you have to check Model Parameters tab:
There you will see your string parameter. Now click on the box under the word Filter (there should be "None") and select Value list. Then click a button from right and here you have fot a table in which you should type all the names you have in your field. After you finish it, click Apply and try to start the model. The drop-down list should appear.