What is the name of this indoor plant?

I have had this plant nearly 20 years. It bloomed once, last year. What is it called and what does it require? The person who gave it to me just said it didn’t like to be moved. It is on a low table in front of a patio door where it receives afternoon sun.

Hi Claire,

 

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Your plant is a succulent houseplant called a Hoya Plant. Here are some plant care tips for a Hoya HousePlant.