Once a custom field is created you cannot delete it*, however you can edit it.
You can also add new custom fields.

To do this, start by navigating to the Settings menu.
From here:

•  Click on the Contacts sub menu.
• Under the Custom Fields tab you will see all of your current custom fields.
• Click on any existing custom field to edit its name.
• Or click the + Add new Field link to create a new custom field.
• After making any changes, click Save Changes.

If you do require custom fields to be deleted, contact the support team to action this for you.