I would like to know how to spell a word with two consecutive U's out loud—like "vacuum". Do we say vee, ay, see, double U or just U, U, em? I'm wondering because if we say "double U" it might be mistaken for the letter "W". But, in fact, the word "vacuum" is not written with a "W".
I have in fact heard (American) native speakers spell two consecutive U's out loud as "double U".
There is no rule. Language is something to have fun with, and there is a wee bit of fun in saying "double" and then the name of a doubled letter instead of saying the name of the letter twice in a row. When spelling out VACUUM, saying "double U" is ambiguous, and there is a wee bit of fun in choosing the ambiguous way to say it.
If you want to avoid ambiguity, of course, you can say "U U". The choice is yours.
However, there is less ambiguity than you might think. The name of the letter W has primary stress only on the first syllable: /'dʌb.l.ju/. When people say "double-X" where X is any letter, they usually fully stress both the first syllable of "double" and the name of the letter. For F, that would be /'dʌb.l.'ɛf/, not /'dʌb.l.ɛf/. For U, that would be /'dʌb.l.'ju/, not /'dʌb.l.ju/.
Also, rhythm is very important in English. Normally when people spell out a word, they give each letter the same amount of time and equal stress. When spelling out CAT, for example, people usually say /'si.'eɪ.'ti/, maintaining a steady beat so each syllable takes the same amount of time. When spelling out AWE, the time spent on each letter stays the same even though it takes three syllables to say the W: /'eɪ.'dʌb.l.ju.'i/; the three syllables of /'dʌb.l.ju/ are spoken quickly, totaling the same amount of time as /'eɪ/. When people indicate a doubled letter with the word "double", it usually makes rhythm irregular. Usually the time spent on the word "double" is a less than the time spent on each letter's name. Sometimes people squeeze "double" into the letter-name's time, or into twice the time of one letter-name, similar to a grace note in music.
But it's not a rule.
By the way, the letter W started as two consecutive U's; hence the name. Back then, U was written V; hence the shape.
There is no inherent ambiguity because Double U (back-to-back letter u's) is pronounced differently from Double U (the letter W).
The letter w is pronounced as one three-syllable word with the stress on the first syllable. Listen here on Forvo. In addition–although not as important–in rapid speech, some speakers of English pronounce W as if it had no l, so dúbba-yu.
To refer to back-to-back u's, the native speaker will pronounce this as two words, with a slight pause between Double and U, and with stress on both words, double and u. In fact, to deliberately avoid ambiguity, they would slow down and make sure the addressee heard it as two words.
This would be true whether spelling V-A-C-Double U-M or some sequence as J-3-Double U-4-underline (J3UU4_) as in a password. One would not usually mistake this for J3W4_, because the W in that would be pronounced differently, as explained above. If the speaker or listener had any doubt, they could always ask for clarification. If there was extreme importance or noise interference they could use a phonetic alphabet.
You could also use the phonetic alphabet to spell it out too if you know it. This type of ambiguity was why these were developed.
In the NATO/ICAO Phonetic Alphabet:
Victor Alpha Charlie Uniform Uniform Mike
When spelling something out loud, the intent is to be especially clear and unambiguous. To that end, even if you used the terminology "double" in general, you should avoid it in this case.
In fact, you may want to (or need to) use a phonetic word spelling in this situation too, so you actually spell out loud, "victor alpha charlie umbrella unicorn mary". Using two different words, though non-standard, helps convey the repetition within the message rather than the message fragment being repeated, which is another source of ambiguity.