Learn Arabic (Modern Standard): كانت تسمية الطفل الجديد سهلة جدا.

تسمية (naming) comes from the Form II verb سمّى (to name). A standard Form II verb usually forms its verbal noun on the pattern taf'iil (like تدريس for teaching). However, because the root of سمّى is defective (it ends in a weak letter), the verbal noun pattern changes to taf'ila, taking a taa marbuuTa at the end instead.

Why doesn't تسمية have the definite article "al-" if the translation implies a specific naming?

The words تسمية الطفل form an Idafa (a possession or "of" phrase), meaning literally "the naming of the baby." The core rule of an Idafa is that the first word (تسمية) can never take ال (al-). It is automatically understood as definite because the second word (الطفل) is definite.

Why is the verb كانت (was) in the feminine form?

كانت agrees with the subject of the sentence, which is the verbal noun تسمية. Even though it describes an action, it ends in a taa marbuuTa (ة), making it a grammatically feminine noun. Therefore, the verb must also be feminine.

If we pronounced the case endings in this sentence, what would the ending on سهلة (easy) be?

It would be pronounced سهلةً (sahlatan) with an accusative ending (two fathas/tanwiin al-fatH). This is because it is the predicate (the describing word) of a كان sentence. While كان leaves its subject (تسمية) in the nominative case, it always forces its predicate into the accusative case.