Yes. At checkout, use the ADD ENTRY tab at the top of the registration form to add as many entries as you need.
If it is a gift, use your own email address
Whoever's email address is on an entry receives the ticket for it. So if you are buying an entry as a surprise, put your own email address on both entries, otherwise the ticket lands in their inbox and the surprise is over.
If you do not have their details yet
You do not need them. Use Speedy Checkout to buy the places now and send the entries on afterwards for each person to complete their own details.