In the UK a jockey can be sponsored, like any other sportsperson, and that logo tends to go on the breeches or undershirt. The owner provides the one-size-fits-all colours and they may or may not carry a sponsor’s logo. Also, the trainer’s yard may have sponsorship which also has to find room. The number cloth will often have the race sponsors name and logo too… There are rules about size, position etc.
As UK horses travel to the racecourse from their training yard, they arrive with bridle, blinkers etc but the saddles belong to the jockeys as they use different sized ones to make the correct weight. I think the number cloths belong to the race course.
The jockeys kit is cared for by a professional valet who does an awful lot of laundry overnight!