You'll want to read this help topic here:
Note: Add to Display is a Model only setting that has no impact on the Model when it's being run as a Model tool outside the Modelbuilder Window.
Rather than opening ModelBuilder each time you want to process your dataset, wouldn't it be better if you could run the model using its tool dialog box, supplying the name of the input dataset by dragging a layer or dataset onto the dialog box, just as you would with a system tool? But when you open the tool dialog box, it displays This tool has no parameters, as illustrated below, so there is no way for you to enter the datasets you want to process.
That entire help topic is focused on solving the question you're asking. I'd suggest you read through it again.
To quote the 3rd paragraph: