PhD branding question [R]

I'm starting a PhD where I will be doing Graph ML (somewhere along the lines of graph signal processing/ graph deep learning.) My eventual goal is research scientist at big tech, or whichever company has a strong research division, where I can continue similar AI/ML work. I have concerns about the job market (both now and in 5 years), and I'm wondering whether I should do my degree under the CS or EE department. For context, my research is within the eecs overlap and this degree would not change my research at all, rather it is a personal branding exercise. I'm thinking about saturation in cs