The only difference is that follow on milk contains added iron. It will do your baby no harm at all. Basically it's no different to first milk. It's often cheaper (see later in my post for why) but us essentially the same product ad first milk. You don't need to change, but it's not going to make any difference if you do.
To understand why, you need to understand a bit about business and marketing.
Formula manufacturers cannot, by law, encourage the use of formula over breastfeeding for baby's first 6 months. So they may not ever discount or offer money-off coupons. They can't advertise first milk in any way, at all. But After 6 months old they can advertise - as long as it's s different product to the one they are not allowed to advertise (first milk)
So Follow On Milk is an invention by formula milk manufacturers, to allow them to advertise. Only 6m+ milks are ever used for adverts. Only 6m+ milks can be offered at a discount price, or with 50% extra free, or with a £1 off voucher. So manufacturers added extra iron to exactly the same product to enable then to have a legitimately different product that they can legally advertise.
There is nothing sinister in the product itself, so don't fear follow on milk. It makes business sence. The only harm formula manufacturers are doing is discouraging breastfeeding by finding a way to allow them to advertise. But if you are already formula feeding then the only real difference between First Milk and Follow On Milk us that follow on milk is 9ften cheaper for the same thing. So I'd use follow on milk just for that reason.