Sorry I am not following
I have a custom component and put in a (old style) text input and a text (label new style, probably doesn't matter but to be exact) and set the Text if this "label" to Textinput.Text
What type of custom component? A canvas app custom component or a PCF?
What does this mean? If this label what?
if this "label" to Textinput.Text.
If I change the edit, the text in the "label" stays the same (in my canvas app a label set to a textinput would change too)
What does "if I change the edit", what is "edit"?
I think you are trying to say, if you have a label inside a Canvas component, and I assign its Default Text value to your Components TextInput.Text value, you want the label to have that value.
I think that is what you are trying to say, and you are saying its not changing the value of the Text label.
Note: please also share pictures and your code/expressions in the properties etc. We constantly catch typo's and wrong placement, so just explaining it isn't enough for us to insure we can help you, as I see no details in your description, assuming I am correct in my translation, that would make it not work.
Meaning it should absolutely set the text, so again ,please share pictures, make sure to include the exact control type in the pictures etc.