I want to place a 2D shirt design on a real photo.

If you want to decribe it, I would say, "creating a mock-up from a photo" would be the way to go (That's a good bunch of the work I do on a day-to day basis, so that's what clients contact me with)
Basically the way to do it, is creating a deformation on a design (preferably with a smart-object) that will follow the shape and creases of the original photo.

So usually, liquifying, warping, using the displacement map filter, and sometimes for more complex objects using 3D (not for a tee shirt though). When the distortion is done, then you'll have to correct the colours and lighting so it appears natural, sometimes blur the design a little, add some grain etc so it looks more like a real image.

You can find ready made mock ups online - but the nice ones are never free, quality vary greatly!
(You can start by searching on Adobe stock, the relevant search term is "templates")

https://stock.adobe.com/uk/search/templates?filters%5Bcontent_type%3Atemplate%5D=1&filters%5Btemplate_type_id%5D%5B%5D=1&load_type=template+lp

I would call it »mapping a design on a (shirt/… in a) photo«. 

Warping, Liquify, Displace … (naturally performed on Smart Objects) are techniques that one could employ for this. 

Please post a sample image.