Basically with Solidworks, I don't think it's possible. On the other hand, you can probably get around it.
You open a drawing, you draw your special frame. Then you create a block.
Then you save this block somewhere where it is easy to find it for you.... and all you have to do is import it according to your drawings and position it on top of your dimension.
I don't know if it will follow your odds (maybe by selecting the two and linking them? But no certainties)
Indeed I want to make a new symbol in the <DIM> like for example the standard functional dimension (the oblong shape around the dimension).
The technique of making a block is not viable because it does not "fit" the size of the odds according to the number of digits. In addition, it does not follow the coast if it has to be moved.