@HelesicPetrand @BjoernRueegg Thank you both for your help on this. I got the following code working. It extracts the display name of a Global Enumerated Value.
com.ptc.core.lwc.server.PersistableAdapter obj = new com.ptc.core.lwc.server.PersistableAdapter(primaryBusinessObject,null, java.util.Locale.US, new com.ptc.core.meta.common.DisplayOperationIdentifier());
obj.load("my_enum_attribute");
Object enumValue = obj.get("my_enum_attribute");
System.out.println("Attribute Value = internal name of Enumerated Value: " + (java.lang.String) obj.get("my_enum_attribute"));
//Returns TA_JBaker
com.ptc.core.meta.container.common.AttributeTypeSummary ats = obj.getAttributeDescriptor("my_enum_attribute");
com.ptc.core.meta.common.DataSet ds = ats.getLegalValueSet();
com.ptc.core.meta.common.EnumerationEntryIdentifier enumerationEntryIdentifier = ((com.ptc.core.meta.common.EnumeratedSet) ds).getElementByKey(enumValue.toString());
com.ptc.core.lwc.server.LWCEnumerationEntryValuesFactory lwcEnumerationEntryValuesFactory = new com.ptc.core.lwc.server.LWCEnumerationEntryValuesFactory();
//System.out.println(lwcEnumerationEntryValuesFactory.get(enumerationEntryIdentifier, java.util.Locale.US));
//Returns: {IS_SELECTABLE=true, displayName=J. Reynolds, display=J. Reynolds, abbreviatedDisplay=J. Reynolds, selectable=true, fullDisplay=J. Reynolds, sort_order=0}
wt.meta.LocalizedValues localizedValues = lwcEnumerationEntryValuesFactory.get(enumerationEntryIdentifier, java.util.Locale.US);
String enum_display_name = localizedValues.getDisplay();
System.out.println("Enumerated Value's Display Name: " + enum_display_name);
//Returns: J. Reynolds