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I'm looking for certain themes for a project of mine and I would like to use sayings like "see no evil, hear no evil, speak no evil". However, I'm having trouble finding more good examples.

What I'm mainly looking for are short sayings that have popular imagery attached to them, such as the above saying and the three wise monkeys. So the saying should be short and sweet and have an image associated with it.

Is there a specific name for these kinds of sayings?

There probably isn't a specific name for the concept you describe.

Webster's new dictionary of synonyms has an entry for saying as the most general term, compared and contrasted to saw, adage, proverb, maxim, motto, epigram, aphorism, and apothegm. I will reproduce it below, but suffice it to say that none of them are exactly what you want: either they are too general or refer to something other than your precise concept.

As far as the 'three wise monkeys' saying, this book on folkloristics simply calls it a proverb. The Wikipedia article on it introduces the very nice name pictorial maxim for the monkeys themselves, and says that this pictorial maxim 'embodies the proverbial principle "see no evil, hear no evil, speak no evil" '. There is a reference to an article (Wolfgang Mieder. 1981. "The Proverbial Three Wise Monkeys," Midwestern Journal of Language and Folklore, vol. 7, pp. 5-38), but I haven't been able to access it. In the book Proverbs: A Handbook, the same author says that

For some proverbs and proverbial expressions like “Pandora’s box,” “The pitcher goes to the well so often until at last it breaks,” and “Hear no evil, see no evil, speak no evil” and the figures of the three monkeys attached to it, art historians, folklorists, and paremiologists have assembled various types of iconographic representations that span several centuries. (source)

The fact that these scholarly sources do not use any term more specific than a proverb to describe “Hear no evil, see no evil, speak no evil” suggests that there is probably no more specific name for the concept you are interested in.

Here is the entry from Webster's new dictionary of synonyms:

saying, saw, adage, proverb, maxim, motto, epigram, aphorism, apothegm can all denote a sententious expression of a general truth. A saying is a brief current or habitual expression that may be anonymous, traditional, or attributable to a specific source <the saying is true, "The empty vessel makes the greatest sound"—Shak.> A saw is an oft-repeated and usually traditional or old saying <full of wise saws and modern instances—Shak.> <the old saw that ignorance is bliss—M. W. Childs> An adage is a saying given credit by long use and general acceptance <if there is verity in wine, according to the old adage—Thackeray> <there's an adage to the effect that a good horse eventually comes back to his best form—Audax Minor> A proverb is an adage couched, usually, in homely and vividly concrete or figurative phrase <accused (in the phrase of a homely proverb) of being "penny-wise and pound-foolish"—Spectator> <we hear, that we may speak. The Arabian proverb says, "A fig tree, looking on a fig tree, becometh fruitful"—Emerson> A maxim offers a general truth, fundamental principle, or rule of conduct often in the form of a proverb <the difference between principles as universal laws, and maxims of conduct as prudential rules—Robinson> <we have reversed the wise maxim of Theodore Roosevelt: "Speak softly and carry a big stick"—Warburg> A motto is usually a maxim or moral aphorism adopted by a person, a society, or an institution as a guiding principle or as a statement of an aim or ideal <William of Wykeham's old motto that "Manners makyth Man"—Quiller-Couch> <he adopted the maxim, "Napoleon is always right," in addition to his private motto of "I will work harder"—George Orwell> The last three terms, epigram, aphorism, and apothegm, commonly imply known authorship and a conscious literary quality. An epigram gets its effectiveness from its terseness and a witty turn of phrase; it characteristically presents a paradox or a cleverly pointed antithesis <what is an epigram? A dwarfish whole, its body brevity, and wit its soul—Coleridge> An aphorism is a pithy epigram that requires some thought <when Mark Twain utters such characteristic aphorisms as "Heaven for climate, hell for society"—Brooks> An apothegm is a sharply pointed and often startling aphorism such as Johnson's remark, "Patriotism is the last refuge of a scoundrel."