PhD branding question [R]

Excerpt

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