Why 'hippo-paw-tamus?'

Solution 1:

Latin potare "drink" is from a Proto-Indo-European root *p(e)h3- meaning "drink" (De Vaan), so it is not related to the root *pet- "to rush" that you mentioned for potamos.

The Greek omikron in ποτᾰμός (potamos) is short and would be pronounced short in Latin. The ō in Latin pōtare, however, is long, so the two o's are pronounced differently in Latin.

As to you paw, I don't recognise that pronunciation. The Oxford English Dictionary (2nd edition) has /pɒ/ for the -po- in -potamus, which sounds just like the po- in the word pot. The first -po- is pronounced /pəʊ/ or /pə/.

It should be noted that any Proto-Indo-European root mentioned, such as *pet-, is not to be interpreted as a guide for pronunciation; pronunciation is extremely likely to have changed between Proto-Indo-European (presumably spoken thousands of years ago) and modern English.