I took List of sovereign states and picked those states which keep word “democratic” in their full name. Then I took the Democracy Index list and joined it to the first list.

Here is the outcome (sorted alphabetically):

State Full Name Democracy Rank Category
Algeria People’s Democratic Republic of Algeria 117/167 Authoritarian regime
DR Congo Democratic Republic of the Congo 162/167 Authoritarian regime
East Timor Democratic Republic of Timor-Leste 46/167 Flawed democracy
Ethiopia Federal Democratic Republic of Ethiopia 124/167 Authoritarian regime
Laos Lao People’s Democratic Republic 157/167 Authoritarian regime
North Korea Democratic People’s Republic of Korea 167/167 Authoritarian regime
Nepal Federal Democratic Republic of Nepal 105/167 Hybrid regime
São Tomé and Príncipe Democratic Republic of São Tomé and Príncipe N/A  
Sri Lanka Democratic Socialist Republic of Sri Lanka 87/167 Hybrid regime
Western Sahara Sahrawi Arab Democratic Republic N/A  

Not a single democractic state (by its name) listed in Democracy index list made it to the category Full democracy as defined by Democracy index.