You cannot leave money or other kinds of property to your pet. The law says animals are property, and one piece of property can't own another piece of property.
Because an animal can't own property, your pet also can't be a beneficiary (someone who receives property) in a will or living trust. If you do name your pet as a beneficiary, whatever property you tried to leave it will probably go instead to the alternate beneficiary or, if there's no alternate, to the person you named as your "residuary" beneficiary (who gets everything not specifically left to other beneficiaries named in the will).
If there's no residuary beneficiary, the property will be distributed to your closest relatives under the "intestate succession" laws of your state, which control what happens to property if there is no will or trust to dispose of it.
So if you name your pet as a beneficiary of your property, in all likelihood the pet will get nothing, and the result may be not at all what you intended.
If your goal is to make sure your pet has plenty of money after you die, you may be out of luck. However, if your goal is to make sure your pet is well cared for after you die, you have several options to consider. If you plan ahead, you can:
You can learn more about these estate planning strategies for taking care of pets on Nolo.com.