Does university name matter in design industry?

I luckily got 2 offers but struggling to decide. First one from a recognised uni in design industry especially for my course which has many graduates work for big brands,interesting modules while the second one is not famous for design but have high student satisfaction rate on unistats and offered me a scholarship( I am an international student so tuition fee is an important factor to think about). I wonder does university name matter when applying for design jobs? And when at uni, does the course itself and tutor help students raise their ability or they do it independently(mostly) when studying? Cheers