Yes, you may name a grandchild as owner of a whole life policy. However, the child's age at your time of death may be a factor in the immediate payout. If your grandchild is presently over the age of 21, there is no problem.
If your grandchild is a toddler now and you die before he reaches a minimum age of 18, 21 or 25 depending on the state, certain laws will apply. It would be essential for you to consult with an attorney in your state to discuss in detail the responsibilities involved in naming a grandchild a beneficiary of a whole life policy.
The money will need to be put in a trust for the grandchild until he reaches a legal age dependent on laws in the state. If the value of the policy is particularly large, discuss with your attorney the ability of putting the money in trusts with payouts at key ages in order to keep the money solvent. This is an especially good idea as many younger people do not invest windfall inheritances. A payout can be given at the age of 18 to pay for college for example. Another payout at the age of 21 or 22 when college is completed or paid for. An additional trust payout may be delivered at the age of 25 or 30 to be a benefit for marriage or home purchase.
A large sum of money can be best left to a minor in the form of trusts as stated above to protect your investment. The trust will also preserve the payout for a duration over several years after the child becomes an adult to avoid misuse of funds.