The vowels on names of God in siddurim are meant to tell you how the name is supposed to be pronounced in each particular case. You may note that the vocalization is not always the same. Most of the time you see the name יהו-ה in a siddur, it is vocalized as ״יְהוָה״ This tells you that this name is supposed to be pronounced with those vowels as "Adonai." The vowels here correspond to the vowels in the word ״אֲדוֹנָי״ (note that chataf-patach is technically a type of shva). In other cases, you might see the name vocalized as ״יֱהוִה״. This corresponds to the name "אֱלֹהִים" and should be pronounced as such.
For example, "אֲדֹנָ֤י יֱהוִה֙" in Genesis 15:2 is pronounced "Adonai Elohim".
The following image shows the connection visually (source):