According to genealogical 'rules' you should record people with their birth name. If a person has changed a name, you should add a Name Change fact in his/her personal card.
At the same time, the person's children would have been born with the new name and would be recorded in the tree as such.
If you would like to add a Name Change fact, please use the instructions in the one of the following FAQs:
How do I add a fact to someone in my online family tree?
* When you add a fact as described, select 'All facts' and find 'Name Change' fact in the list.
Besides you can add additional names editing the person's profile, using the following instructions.
If you are editing your tree online on your family site:
Open the person's card in the tree, and click on 'Profile' button on the left side panel.
On the profile page click on 'Edit profile'.
Here you will be able to use the 'Additional names' option.
If you are editing your tree in the Family Tree Builder software:
Find the person in the tree and double-click on the personal card to 'Edit details' window.
Click on 'Names' button and add additional data according to your preferences.