Use SchemaScanner to get attribute names in attribute{}.name list on the <Schema> output port.
FeatureMerger, Output port of SchemaScanner to Requestor, <Schema> port of SchemaScanner to Supplier, join on fme_feature_type_name to merge the attribute{}.name list to the original features.
AttributeManager with Set Conditional Value on initial attributes, test if Attribute Has a Value (or if it is equal to INTERSECTS) and set attribute value to the corresponding list element from attribute{}.name.
I have attached a sample workspace to use as a starting point.
@rhysdixon8 the solution above using the attribute{}.name works well, but might get bit tedious if you have 70 attributes. @Takashi Iijima often has a good solution using the NullValueMapper for these types of problems but I couldn't see that here.
PythonCaller and a short python script might help: see the attached example workspace (FME 2021.2)