Yes, most (all I am familiar with) hotel programs are similar to airline frequent flyer programs in that you sign up for the rewards program and receive a number that you then enter into your reservation (or provide to the hotel front desk personnel if someone else makes your hotel reservations and will not enter your rewards number) to get hotel points for the stay. These hotel points are based on the amount of the stay, regardless of what credit card is used for payment. You are lucky that you can use your personal credit card for the hotel and get reimbursed; a lot of us are stuck using a corporate travel card for hotels.

Another option, if you prefer to accumulate airline miles rather than hotel points is to enter an airline FF # instead of a hotel loyalty program number when you stay at a hotel (with Hilton HHonors, you can get both airline miles and hotel points for the same stay, but with most other programs, you have to choose miles or points for a stay, but can change this for each stay.

You can find out more about the programs by going to each chain's website and/or checking out the very informative sticky threads on the individual hotel threads on this forum.

Hope this helps!