Each different character has its own meaning. Two characters would means different thing (may or may not be related) even if they are pronounced the same. To figure out, you may refer to a dictionary. It would list out all possible writings for a particular meaning. For ぞう for elephant, you will not find 三 in the list. For names, just remember them one by one. Even Japanese cannot tell which character is used.

I saw your website. Though you searched for "三 ゾウ", it does not mean all returned search result are written as 三 and read as ゾウ. To know the actual written form and reading, you must check the result entry one by one. One the right part of the search result I saw four different characters that can be read as "ゾウ" with different meaning. For elephant, the written form is 象

As Andreas already said, 三 never can be "elephant" though 三 is read as ぞう especially when it's used for names. Lots of kanji are read in several way, like 三 (さん、み、ぞう、etc) and there are many kanji which are read ぞう. Please learn about it step by step. I hope this was helpful.

Sorry I don't know why it's not linking but if you look up 三 on jisho you will see elephant alongside 3.

Hi Andreas, thank you for your response. The website you mention above is where I saw that 三 can also be elephant. http://jisho.org/search/%E4%B8%89%20%E3%82%BE%E3%82%A6 I'm confused!