A dragonfly is the insect that is sometimes called a darning needle. They were given this nickname because some cultures link them to evil things.
The Devil's Darning Needle is the Dragonfly
There is no physical difference between a dragonfly and a darning needle. The name "devil's darning needle" was given to dragonflies in Europe because they were thought to be evil or sinister.
devils darning needle
people thought if you fell asleep outside dragonflies would sew your eyes and ears up
Darning thread and needle are used for repairing holes or worn areas in fabric, particularly in knitted or woven items. Darning involves weaving the thread over and under the damaged area to create a sturdy patch that blends with the surrounding material. This technique not only extends the life of clothing but also allows for creative expression in mending.
Next to butterflies, dragonflies are some of the most colorful insects in the world. The darning needle dragonfly comes in several varieties and colors, one of the most striking is very bright red, with translucent wings.
mosquito
What you're describing sounds like a "tapestry needle" or a "darning needle." These needles have a flat end, which allows for easier threading of thicker yarns or fabrics. Unlike standard sewing needles, which have a pointed end, the flat end is designed for specific tasks like weaving or mending.
because they are various large insects of the order Odonata or suborder Anisoptera, having a long slender body and two pairs of narrow, net-veined wings that are usually held outstretched while the insect is at rest. Also called regionally darner, darning needle; Also called devil's darning needle, ear sewer; Also called mosquito fly, mosquito hawk; Also called needle, skeeter hawk; Also called snake doctor, snake feeder; Also called spindle.
To use a needle and thread could be called sewing.To use a needle and thread could be called quilting. To use a needle and thread could be called embroidery. To use a needle and thread could be called suturing.
The clear plastic section of the needle is called the needle hub. It is the part of the needle that attaches to the syringe and holds the needle in place.
....you answered your own question - it's called "threading a needle".