Are there general rules for forming nouns that refer to the one performing the action of a verb, such as cut -> cutter, run -> runner, "Jack the Ripper", etc.? I have been searching online but have only found guidance on forming gerunds, possibly because I don't know the grammar terminology to ask the right question.
There is no one-size-fits-all solution, and you have to be familiar with many patterns. To add to what Angelos have already mentioned, one important pattern is masu-stem as a noun.
- のぞく to peek / のぞき peeper
- 魔法を使う to use magic / 魔法使い magic user → wizard
- 相撲を取る to play sumō / 相撲取り sumō wrestler
- 羊を飼う to raise sheep / 羊飼い sheep raiser → shepherd
"Jack the Ripper" is 切り裂きジャック in Japanese, and 切り裂き is the masu-stem of the verb 切り裂く ("to rip/tear").
There is no regular way of doing this. While the suffixes ～人｛びと｝, ～者｛もの｝ (generally used with kun'yomi), and ～者｛しゃ｝ (generally used with on'yomi) are common, often you simply need to use a relative clause.
裏切り｛うらぎり｝者｛もの｝ - traitor (from 裏切る｛うらぎる｝, 'betray')
旅人｛たびびと｝ - traveller (though this actually uses a noun)
目撃者｛もくげきしゃ｝ - witness (somebody who witnesses something, and again 目撃 is actually a noun)
切｛き｝る人｛ひと｝ - cutter, 'person that cuts' literally
Even the first example technically uses a noun form of the verb, too.