One way that you could make the logo appear between the person and the white background would be to create a layer mask on the logo that reveals the person:
Open the image of the person on the white background.
Place the logo (File > Place Embedded...)
If the logo has a background, the in the Properties panel (Window > Properties) in the Quick actions section (you may need to expand the Properties panel down in order to see this section), click remove background.
Temporarily turn off visibility of the logo layer (so that it doesn't become part of the selection later) by clicking on the eyeball to the left of its layer.
Select the person layer in the Layers panel.
With any of the selection tools selected, you'll see Select Subject in the Options bar (if it's not visible, go to Window > Options). Click Select Subject (you can use the dropdown menu to the right of Select Subject to select whether you want the selected created from the Device or the Cloud).
While the marching ants (the active selection) showing, toggle the visibility of the logo layer back on by clicking again where the eyeball was, select the logo layer in the Layers panel, and go to Layer > Layer Mask > Hide Selection.
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