Ultimate Park Hopper Passes are sold two ways: as a package (either included or added) with your WDW room reservation through CRO or WDTC or as a counter sale you purchase upon check in at your resort front desk. The two methods have different restrictions.
When you purchase your UPH's through CRO/WDTC, they are directly tied to the entire length of your reservation and the number in your party; hence the length of stay pass must be purchased by all members of your party (except for holders of AP/PAP's) and must equal the number of nights reserved. Holders of valid AP/PAP's are exempted from this requirement. You must purchase UPH's to cover your arrival day straight through to your departure day. One advantage to purchasing this way is you will get a slightly reduced advance purchase price for each UPH you buy.
If you wait until resort check in to purchase your UPH, you will pay a little more for your UPH's but it may be more advantageous to you since you may have either your arrival day or departure day removed thus saving you some money over the advance purchased UPH's. If your UPH's were purchased as part of a Disney package (Dream Maker, Resort Magic, Grand Plan, etc), you cannot change them to drop a day.