Here's an expression which will do the trick - just substitute your actual layer name below:
attribute(get_feature('YOUR_LAYER_NAME','DIST_ORIG',"NAME"),'DIST_ORIG') then true
To break this down:
this part will fetch the first feature from your layer where the DIST_ORIG value matches "NAME" (eg, the value in the "NAME" column for the current feature). If there's no matching features found, nothing will be returned by this function.
We then need to do a little trick to convert this to a condition we can use in the
CASE WHEN / ELSE / END statement. So I've wrapped the
get_feature call in a
attribute function, which will return the value in the specified field from the feature returned by
get_feature. So this will either be a value from "DIST_ORIG" if a feature was found, or
NULL if no feature was found.
CASE WHEN / ELSE / END is just used to directly convert the result to a true/false value.