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https://en.wikipedia.org/wiki/Iberis

Iberis.

Thank you; I found that too, of course, but I am  sure that it is not the same thing. I can't see how one could use that flower, even dried, to make trees.

Is there no other flower than Iberis, that has the nickname "candytuft" or "sesame bloom" in the USA? Something like this: https://ohyourelovely.com/search?q=sesame

And my question still is: can someone tell me the botanical name of that flower, so that I could find the commercial name that is used in MY part of the world? Thank you!

Common names

You have just run head-long into the problem with common names. Looking up candytuff, sesame bloom, and or Iberis the plants and flower stalks don't look like the pictures in the link. The pictures remind me of a plant called baby's breath, maidens breath, or showy baby's breath, Gypsophila elegans. I'm not sure that is what your are looking for by you might give it a try.

Dick

Candytuft

The plant sold dried as “Candytuft” for floral arrangements is not Iberis Sempervirens. I suspect that like the other names used for it—“Sesame Bloom” and “Sugarbush”—Candytuft is a made-up name for marketing rather than a recognized botanical term. In any case, you can find places to buy it online using those former terms. Most sell it for floral arrangements, but there is at least one model railroad source that carries it, a small online firm called Scenery Solutions. Two other natural plants traditionally used as material for making model trees and shrubs are caspia and babysbreath. All of these are dried with flowers intact that serve as leaves when made into miniature trees. But today modelers are more apt to use Seafoam (Zeechium Teloxys Aristata) for tree armatures and apply foam or flock as leaves.

Thank you

for all these informations!

Sesame Bloom is also used as

Sesame Bloom is also used as an alternate name for Virginia Pepper weed (Lepidium virginicum) AKA peppergrass. I don't personally see how Candy tuft (Iberis sempervirens) could be used as an armature, but I suppose it has potential. The pepper weed is hardy and pretty rigid, so it makes great tree armatures, with or without the seeds. It's also edible when fresh, tasting like black pepper or horseradish, which also gives it the name Poor Man's Pepper.

Pepperweed definitely did not earn the name "candy tuft", but one story I came across mentioned the "candy" may be derived from "Candia", an old name for Crete. I can imagine pepper weed would feel quite at home there.

It grew quite well as volunteer plants in my yard and around my neighborhood in Akron, Ohio. I found it liked well drained soil and a lot of sun. It's easy to gather a bag full of the stuff from an empty lot or field in summer or early fall. And it will work for any scale.

Another common plant that can be used is "Autumn Splendor" sedum. The dried flower head can be harvested in early winter. It's a little coarse for N scale but it's decent enough to make background trees.

Another I've used is the flower head from the spirea bush. It's woody enough to keep its shape as a model tree. It may be a little small for larger scales, but I've seen some pretty big flower heads, so your mileage may vary.

I also found some seed stems from what I thought was a variety of maple tree I could use for dead or scrub trees, but I have yet to identify it positively. You can find lots or interesting things just by walking around and keeping your eyes open.

Can be difficult to find

This question comes up from time to time and most hobby shops (the ones with dried floral departments) will have no idea what you’re talking about. As Ed and others pointed out “Sesame Bloom” is what you want. Some places may have “Candy Tuft” or “Pepper Grass” but what you’ll end up with may or may not be the same material made famous by Dick Elwell. 
Here’s a modeling place selling “Candy Tuft” that appears to be what we need:
Candy Tuft

I don’t fully get why this stuff is so hard to find but, my understanding is that these plants have a fairly short growing season and suppliers run out of it quickly. As I write this in April, there’s a seller on Etsy offering the correct stuff:

Sesame Bloom
However, they currently don’t have the best color in stock. Yellow and basil might work, but the other colors offered are far to stark for my taste. I like using the “natural” or undyed bloom which can be sprayed with subtle, more realistic colors. (Plus, at $18 for a 4 ounce bunch, I’d rather not settle on color!) If neither of these are available or usable, show the links to a local florist and perhaps that can get what you want. 
I have a couple sprigs to give you an idea of what dyed vs natural looks like:

Hope that helps!

Hobby Lobby

Hobby Lobby has been a great help with DIY trees and ground cover for me.

Dried Baby's Breath has been very easy to paint trunk,  spray branch's and sprinkle some kitchen herbs such as Paprika and such.

Deer Moss in a blender supports ground cover in swamp or wet areas.

Most H-L stores have clearance area in back.

Boudreaux,  B.C.E.

Cheap women's hair spray is great adhesive.  a little goes a long way,