Double blindedness in a fully remote trial
Double blind basically consists when the patient does not know to which condition it belongs (control, treatment A, treatment B) and the professional does not know to which group he/she is administering the treatment (control, treatment A, treatment B).

The double-blind designation is not based on the fact that the initial level of depression is not assessed. (I guess you know it and it has been erroneously specified in the question).

In online studies this denomination is not usually used although of course it is not incompatible. (The issue is that this denomination is not usually used because the trial is not common either).

In short I do not see problem with the double blind designation.

On the other hand, it would be necessary to pay close attention to the clinical level and the characteristics of the intervention (you do not specify, is the intervention also remote?).

In any case sounds very interesting.