Want to make a large felted bag with stash using lots of yarn with purples in it. I have lots of yarn from a friend not labeled. Can you felt yarn with mohair in it?

Possibly, but without labels it’s hard to tell exactly what it is. To felt you want the majority of the fiber to be feltable wool. Superwash wool, bamboo, cotton, silk, acrylic, etc will not felt. The best way to tell if unknown fibers will felt is to make a swatch and test it out.

Mohair will felt. I second Jan’s suggestion of a swatch, but I’d make it the shape you want a pocket. If it does felt, your pocket is ready, and if it doesn’t, you know.
Even if some of your yarn doesn’t felt, you can work…oh, shoot, I think it’s called brick stitch, where you (this will be clear as mud, but I have no way of drawing a diagram):
knit two rows with yarn that does felt,
change yarn to something that doesn’t felt, knit 5, (slip the next stitch, k 5) across,
repeat three more times, then
go back to the feltable yarn, knit 2 rows (you may want to knit the one from the way-down row more loosely.)
Change to the non-felting yarn and knit 2, slip the next stitch, knit 5, slip the next stitch…and do four rows like that, then go back to the felting yarn…and so on until you get the piece you want.
What you get is offset “bricks”. When it felts, if the non-felting yarn really doesn’t felt, you get a really thick, bubbled-looking fabric that works really well to cushion laptops and things like that. Even if everything felts, you’ll still have the color pattern. You can also just repeat Rows 1-6, without offsetting, and you’ll get straight columns of felted stuff with bubbles between.

I agree with Jan that you will need to knit a test swatch and see if it felts. It is helpful to felt a test swatch even if you know the yarn will felt so that you know how much it will shrink in each direction so your bag doesn’t end up oddly shaped.
My other comment was going to be that I have been warned away from making a stash bag unless all the yarn is the same brand and weight b/c otherwise they may felt differently and mess you up.
I have ziploc bags full of wool ends I had been saving for that very purpose…