QGIS set fixed ID name with autoincrement in data attribute table

Open the layer properties and go to the Attributes Form tab on the left.

Select the "ID" field and go down to Defaults.

We're going to add an expression here to auto-increment the field. This would be easier if it was just a numeric field but because it is a text string it will take a little more fine-tuning, but that's OK.

Before I get into it, the idea is that we're going to extract the numeric part of the string and convert it to an actual number. That way we can find out what the current max is and then increment that. Then we'll add that back on to the generic string. But we have to be careful when doing that because of the leading zeroes. Also because this will need to be set to auto-update, we have to add a catch to prevent it overwriting pre-existing IDs if you edit those features.

So the expression box add the following expression:

IF("ID" IS NULL, --this checks if there is already an ID value

'DT.C.10_Strand_' || lpad(to_string(maximum(to_int(right("ID", 3)))+1), 3, '0'), --this section adds the incremented number, padded to the left for leading zeroes

"ID") --this is in case there is already an existing ID

Then make sure the Apply default value on update box is checked.

EDIT: I see @Taras has added a comment which might be more elegant than my hacky code

EDIT 2: I was inspired by @Taras's better code to update my answer, thanks @Taras.