I try to look at it like other people riding my favorite horse is just extra love and attention for them! That doesn't stop me from bringing her an extra treat now and then, though ;)
Bring him a cookie/treat every day you see him, and make sure you give him lots of grooming.
Make sure you always think about it in terms of the horse, not in terms of you - as in, he's just doing his job. If other people love him too, that's because he's a gem, and it doesn't diminish the love you give him at all. He needs all love!
Often times, our riders will take a work to ride opportunity so they can spend more time riding your favorite lesson horse which also decreases time other people ride him or her. Sometimes, owners can do leases on horses in their lesson program and said lease horse could be ridden by you and only you! Hope that helps!