retain the color... definitely not white.

The stone color did not change and no to white mortar .

It looks fine the way it is, but it is clearly not meeting your expectations. You can discuss this with the person doing the work, but I agree with the other commenters, white mortar will not be an improvement.

I see stone color change On the exterior stone. This is with grey mortar.

No white mortar.

The first photo appears to be a display.

The second photo appears to be a sample in a house.

The photos above appear to be the stone installed on an exterior.

The lighting is going to impact how the stone looks. Can you be more clear about the problem?

I see smudges of grey mortar on the stone after installation on exterior

does the smudges come off eventually is it going to be like that

You can't compare the color like that!

Take that sample board and hold it up to the showroom fireplace ... then take that same sample board and hold it up to the stone on that house.

If the house isn't yours, ring the doorbell and ask if you can place your sample board next to it. I've never had a homeowner refuse to help with something like that.

Also if a stone has been installed outside for many years, you will get staining from dirt and irrigation water and maybe fading from the sun.

Can you post a close-up photo of the smudges?

That's a different issue than the stone actually being a different color than the display. Or the issue of the stone color possibly looking different because the mortar color is different than the display. Or the stone looking different because of the natural versus artificial lighting.