The process of registration of a child under 18 years old to be a British Citizen is called Registration, while it is called Naturalisation for adults.
Before making a Registration application, you should check if your child is automatically a British citizen. A child can already be a British citizen if they were born in the UK or have a British parent. Moreover, again, they will get British Citizenship automatically, if your child is born after you obtain permanent leave in the UK, such as:
If you certainly know that your child is not already/ automatically a British citizen, whether or not you can apply for citizenship for them depends on where they were born and your immigration status. Please contact us for further information.