How to get rid of color profiles at export , have matching appearance in Photoshop?

Photoshop will always use a colour profile. If an image has no embedded profile, Photoshop will either ask which profile to assign or assign the default working space profile (which will often be incorrect), depending on the color settings in Photoshop for missing profiles. 
The safest way to ensure images opened in Photoshop display correctly is to set Photoshop’s Colour Management Policies (in colour settings) to Preverve Embedded Profiles and then ensure that any image (including renders) that are exported for use in Photoshop have an embedded colour profile. That does not have to match an existing Photoshop default profile.

On export from Designer the images have no embedded profile so it will need to be assigned on opening in Photoshop. For Basecolor that will be whatever you exported the image as e.g. sRGB. For other maps such as height etc then if you exported them as RAW you will need to assign a linear greyscale profile in Photoshop. If you don’t have one, you can create that profile in Photoshop by going to Color Settings - Working spaces - Gray - and choosing Custom Gamma and setting it to 1.0. Save that profile and you can assign it on opening. 

When comparing the linear Photoshop view to Designer’s view, remember to uncheck Designers 2D view ‘Consider image in sRGB workspace’

Dave