The naming of an acid depends on the suffix of the cation or anion name (please note that the term “stem” refers to the root word of the ion: if the ion’s ending is “-ide” then the name follow the following rule; hydro- (stem) - ic acid. If the ending. Just like the fluoride ion, which ince the rule is applied becomes hydrofluoric acid. If the naming is “-ite” then the name follows this rule: (stem) - ous acid, for example NO₂ or nitrite ion. Once the rule is applied it becomes nitrous acid. If the ion ends in “-ate” then it follows the following rule: (stem) –ic acid. Like the sulfate ion, which once applied to the rule becomes sulfuric acid. Other common examples are: hydrochloric acid for hydro – (stem) - ic acid rule, sulfurous acid for (stem) – ous – ic acid, and carbonic acid for the (stem) – ic acid rule.
If a base contains rhe ion OH-¹ then it keeps the name and just add hydroxide, a fine example is the formula Al(OH)₃ or aluminum hydroxide. (The rule only works if it contains OH)
In conclusion, the name of a base depends if it contains OH (Hydroxide) or not, and the name of an acid depends on the ion’s ending.