Answer: I am not familiar with a perennial with the common name of "forget-me-not", but there are several annuals with that name or a variation of it. These may come back every year from seed to make a self-perpetuating patch and in that sense are "nearly" perennial. There is also a reliable perennial, Brunnera macrophylla or Siberian Bugloss, with blue, forget-me-not-like flowers although the plant itself is not at all similar. Perhaps that is what you have. This is a sturdy vigorous plant for rich soil in sun to part shade, but it needs a moist location if it is in a sunny spot. It may also self sow and make a little patch if it is happy where you plant it.
There are many, many perennials and a wide variety of common names for them. Some have two names (or more) and in some cases one name may mean two entirely different plants depending on who is using it. For this reason, it is a good idea to find out the Latin name of your plant as well as the common name being used for it. Once you know this information, it is a good idea to research the plant a bit to see if you can provide it with the growing conditions it needs to thrive. If you don't have the right conditions, then it will in all probablility be an annual for you -- even if it is normally considered a perennial! By the same token, perennial gardening is often an experiment in that your garden is full of microclimates and differing conditions, so it is often worth trying a plant in more than one location to see where it will grow best for you.
If you are just starting out, you might find "Perennials for Dummies" by Marcia Tatroe ISBN 0-7645-5030-6 helpful. With a bit of experioence, you might prefer a book with more detail such as "Perennials for American Gardens" by Ruth Rogers Clausen and Nicolas H. Ekstrom ISBN 0-394-55740-9. Enjoy your perennials!
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