Help: dyeing yarn

Hi everyone!
I wondered if anyone could help me with dyeing wool yarn.

I have recently bought a bulky yarn which is 100% sheep wool (similar to felting merino wool). The yarn seemed a dark bordeaux shade in the picture, however, it arrived bright red. I want to dye it to mute and darken its shade but afraid of ruining or felting the wool…

I wanted to ask if you have any tips for dyeing wool yarn? Do you have any recommendations for dye brands?

Attached here an image of the yarn.image|900x1200

I’ll appreciate any help.
Thanks in advance!!
Romi