Correct. Adidas' brand name is uncapitalised, as shown below, with a lowercase "a" at the beginning of "adidas".
The uncapitalised Adidas brand name is usually placed below one of their graphical motifs: the trefoil logo or the performance logo. I have yet to discover a reason why Adidas use a uncapitalised brand name: I would speculate it's because an uncapitalised brand name looks more attractive than a capitalised one.
Adidas' principle competitors: Under Armour, Nike and Puma, fully capitalise their brand names as "UNDER ARMOUR", "NIKE" and "PUMA". So, I suspect, Adidas had the option of picking "adidas" or "ADIDAS" as their brand name, both looking more attractive when printed on their products than "Adidas".
Sportswear brands that follow Adidas' example and use an uncapitalised brand name are: Umbro "umbro", Asics "asics", and New Balance "new balance". I could only find two brands which use an capitalised brand name, Reebok and Kappa; incidentally, Reebok are owned by the Adidas Group. One reason these brands may use a capitalised brand name is because they feature a double letter combination: "ee" and "pp"; pure speculation however.