Learn English – Right word to describe this kind of search

It's an idiom, not a word, but we sometimes say one's mind is in the gutter.

EDIT: As for specific words, one could say, "You have a dirty mind!" My computer's on-board thesaurus offered these synonyms for that sense of the word dirty:

indecent, obscene, rude, naughty, vulgar, smutty, coarse, crude, filthy, bawdy, suggestive, ribald, racy, salacious, risqué, offensive, off-color

Of those, I think suggestive, vulgar, smutty, risqué, and off-color perhaps fit most closely with what you're getting at.

As an aside, ELU had an earlier discussion about the word naughty.

Allegory

1. a poem, play, picture, etc, in which the apparent meaning of the characters and events is used to symbolize a deeper moral or spiritual meaning 2. the technique or genre that this represents 3. use of such symbolism to illustrate truth or a moral 4. anything used as a symbol or emblem

The literary device is known as a 'Symbolism in literature' or a variant.

The symbolist movement in literature / by Arthur ... . Symons, Arthur, 1865-1945 states:

Symbolism in literature really is: a form of expression, at the best but approximate, essen- tially but arbitrary, until it has obtained the force of a convention, for an unseen reality ap- prehended by the consciousness. It is some- times permitted to us to hope that our conven- Rtion is indeed the reflection rather than merely the sign of that unseen reality.