How do you guys pronounce a double pee? And, how is it different from just a (lonely) pee?

Please learn the difference between P (the letter) and pee (=urinate)

In case of doubt about pronunciation, use forvo.com

Phillippu would be pronounced almost like phil, lip, oo

with a single P people may be tempted to say phil eye poo

Double-consonants almost never sound any different than single consonants.  Shaming and slamming have the same m sounds.  the use of single versus double is typically a spelling rule, one which depends on the word without the next syllable. if the word is shame and ends in e, then single m is used to make shaming.  If the word ends in the consonant, the usual (or regular) form is a double-letter. slam, slamming.

Part of the reason for this convention or rule is to tell what vowel sound ought to precede the suffix.  Dine dining (still a long i), but dinner (short i).  The removal of the final -e takes away the info that the preceding vowel is a long vowel, so we use a single consonant to still tell that it is a long vowel.

As a general thing, yes, you have the correct understanding.  Sadly, though, English has many exceptions for any rule, and you have to learn them because they usually are not obvious.

In the version of English which I hear every day in southern England there is no difference between 'p' and 'pp'. I have not heard any differences with speakers from other parts of the wide-spread English-speaking world.

There was an advert on TV for a chocolate bar: "P-p-p-pick up a Penguin" - but but that was for comic effect.

I pronounce them the same but I'm nor sure that's correct .