Onomatopoeia is not the same thing as the name of the sound something makes. Names of sounds include such words as yawp, cry, bellow, and whistle.
Onomatopoeia is the written approximation of how a word sounds. Refer to the work of cartoonist Don Martin for examples.
Sometimes these two types of words are one and the same, such as screech and bang.
What vocalizations do dogs produce? If you'd want to use a word that appears in the dictionary, you'd write that it barks. If you wanted to describe it via onomatopoeia, you'd write that it says "Woof!"
Now, as for ambulances. The term most often used to describe the sound of their siren is probably "wail." But if you wanted to write out how they sound with onomatopoeia, there are no set rules on what to write or how to spell it. "WEE-OO WEE-OO," "Wheeeeeeeoooooawww," and "WEEAW WEAAW WEEAW" are all acceptable ways to express it, and there are many more.