Renting a car in Kamakura involves some risks. In some cases, rental shops might not be aware of specific requirements. However, you can still rent a car, but it's advisable to have some knowledge of Japanese to complete the necessary forms and write your name in Japanese characters. Knowing a few characters of your name should suffice. Keep in mind that driving is on the left-hand side, and road signs are mostly in Japanese.
When renting a car in Kamakura, you will typically need to provide a deposit as it's a standard practice. Rental agencies are quite strict about this requirement. If you decide to rent a car, you can book one online 24/7. Websites like this one can help you with your car rental needs.
Booking a rental car in advance can often lead to more affordable rates in Kamakura and Japan in general. For instance, the international company "Dollar" offers reasonably priced car rentals in Kamakura, around 5500 JPY.