Words that have double meanings

Words that have double meanings in English probably have two words in Spanish.
For example, "left". "I left my phone at home," versus "Turn left at the light." Is there a name for this phenomenon or a list of common ones?

In English, 'left' can be a past-tense verb or it can be an adverb. The two words are called homonyms (each has the same spelling and pronunciation, but different meanings). The two different meanings have two different translations into Spanish.
There are lists of common homonyms, but very few that translate the different meanings into another language. A dictionary will be your best friend, after you figure out how the word is used in a clause (its role/grammatical usage). Once this is known, you'll find the correct translation. By the way, a verb is listed in a dictionary only in the infinitive form.

You'll first need to convert 'left' (past tense) to 'leave' (infinitive) before you can discover that 'salir', 'irse' or 'quedarse' is a possible translation (you'll want to use the last one, in this case). Remember to conjugate the verb back into the past tense.

The adverb '(to the) left' is 'a la izquierda'.

In your question you asked about the word(s) "left": as Rusty says, your question is a case of 2 independent words that happen to be pronounced and spelled the same; that is, homonyms. Each word has its own meaning and its own translation equivalent in Spanish.

The other half of the issue is individual words (the "same" word) that have more than one possible meaning or usage. As an exercise, look up any very common English word in your favorite English-only dictionary, for example "run", "get" or "time" and you will see a very long list of meanings and usages. While it's possible that a few of the meanings and usages may share the same translation equivalent in Spanish, usually at least some of the individual meanings or usages have unique translation equivalents in Spanish.