Besides looking like a sun,
they also follow the path of the sun.
(Heliotropism.)

Mimicking implies it’s changing its appearance to copy the appearance of the sun (like a chameleon). Which sunflowers do not.

Look at the ancient hieroglyphs where the sun was represented by a circle with spikes protruding from it. That is more or less what a sunflower looks like. Originally they were yellow in color — once again replicating the sun

Quite the opposite. The coloring is meant to provide an inviting ‘target’ to insects (bees, etc.) that will land, pick up drop off pollen, allowing for the spread and future generations of the sunflower. The flowers are essentially shaped as they are to make it easy and attractive for the insects to land.

It’s sort of similar to malke peacock plumage, which attracts female peacocks in order to breed. It’s all about survival of the species.

The follow the sun.

The color, the pedals and style. They certainly remind me of the sun. My sister loves and collection all things sunflowers, which I help her to get. :)

The reason they are called sunflowers has nothing to do with appearances. There are many different kinds of sunflowers. The one thing they have in common is they are sun worshippers.
As pointed out by @raum, they turn toward the sun. The bloom turns toward our solar source. That is the inspiration for their name.

Young stems/leaves follow the sun for photosynthesis. Mature heads face east, I suppose one could say to greet the morning sun.

By the way if anyone wants to see wild flowers you can take a drive through the high planes late spring to mid summer.

There is no reason.