I've seen that in some verbs a letter is repeated in the singular subjects like in in koken (ik kook, je kookt, hij kookt) but it doesn't happen in komen that has the "o" in the same position. And it happens too in slapen for example. What's the rule?

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The spelling rule follows the pronunciation and involves doubling of vowels or consonants. The doubling of letters has to do with the way we divide words into syllables.

This is the pattern for long vowel sounds:
slaap - slapen
kook - koken
neem - nemen
duur - duren (to last)

This is the pattern for short vowel sounds:
pak - pakken (to take, to grab)
stop - stoppen
bel - bellen (to phone)
luk - lukken (to work out)
zit - zitten

'Kom - komen' is an exception, because 'kom' is pronounced with a short o and 'komen' is pronounced with a long o.
That is why we write:
kom (short) - komen (long)