diff --git a/gap/elements.gi b/gap/elements.gi
index 5ecd166..2fdb0a1 100644
--- a/gap/elements.gi
+++ b/gap/elements.gi
@@ -17,7 +17,7 @@ InstallMethod( PrintObj, "for a quasigroup element",
 function( obj )
     local F;
     F := FamilyObj( obj );
-    Print( F!.names, obj![ 1 ] );
+    Print( F!.elmNamePrefix, obj![ 1 ] );
 end );
 
 InstallMethod( PrintObj, "for a loop element",
@@ -25,7 +25,7 @@ InstallMethod( PrintObj, "for a loop element",
 function( obj )
     local F;
     F := FamilyObj( obj );
-    Print( F!.names, obj![ 1 ] );
+    Print( F!.elmNamePrefix, obj![ 1 ] );
 end );
 
 InstallMethod( \=, "for two elements of a quasigroup",
diff --git a/gap/quasigroups.gd b/gap/quasigroups.gd
index aee54d3..aa161a6 100644
--- a/gap/quasigroups.gd
+++ b/gap/quasigroups.gd
@@ -99,8 +99,9 @@ DeclareOperation( "NormalizedQuasigroupTable", [ IsMatrix ] );
 DeclareAttribute( "CayleyTable", IsMagma );
 DeclareOperation( "QuasigroupByCayleyTable", [ IsMatrix ] );
 DeclareOperation( "LoopByCayleyTable", [ IsMatrix ] );
-DeclareOperation( "SetQuasigroupElmName", [ IsQuasigroup, IsString ] );
-DeclareSynonym( "SetLoopElmName", SetQuasigroupElmName );
+DeclareOperation( "SpecifyElmNamePrefix", [ IsCollection, IsString ] );
+DeclareSynonym( "SetQuasigroupElmName", SpecifyElmNamePrefix );
+DeclareSynonym( "SetLoopElmName", SpecifyElmNamePrefix );
 DeclareAttribute( "ConstructorFromTable", IsMagma );
 DeclareOperation( "CanonicalCopy", [ IsMagma ] );
 
diff --git a/gap/quasigroups.gi b/gap/quasigroups.gi
index 2414579..54df1f6 100644
--- a/gap/quasigroups.gi
+++ b/gap/quasigroups.gi
@@ -187,7 +187,7 @@ function( ct )
         NewType( F, IsQuasigroupElement and IsQuasigroupElmRep), [ i ] ) ) );
     F!.set := elms;
     F!.cayleyTable := ct;
-    F!.names := "q";
+    F!.elmNamePrefix := "q";
     # creating the quasigroup
     Q := Objectify( NewType( FamilyObj( elms ),
         IsQuasigroup and IsAttributeStoringRep ), rec() );
@@ -196,7 +196,7 @@ function( ct )
     SetAsSSortedList( Q, elms );
     SetParent( Q, Q );
     SetCayleyTable( Q, ct );
-    SetConstructorFromTable(QuasigroupByCayleyTable);
+    SetConstructorFromTable(Q, QuasigroupByCayleyTable);
     return Q;
 end );
 
@@ -225,7 +225,7 @@ function( ct )
         NewType( F, IsLoopElement and IsLoopElmRep), [ i ] ) ) );
     F!.set := elms;
     F!.cayleyTable := ct;
-    F!.names := "l";
+    F!.elmNamePrefix := "l";
     # creating the loop
     L := Objectify( NewType( FamilyObj( elms ),
         IsLoop and IsAttributeStoringRep ), rec() );
@@ -235,22 +235,24 @@ function( ct )
     SetParent( L, L );
     SetCayleyTable( L, ct );
     SetOne( L, elms[ 1 ] );
-    SetConstructorFromTable(LoopByCayleyTable);
+    SetConstructorFromTable(L, LoopByCayleyTable);
     return L;
 end );
 
 #############################################################################
 ##
-#O  SetQuasigroupElmName( Q, name )
+#O  SpecifyElmNamePrefix( C, name )
 ##
-##  Changes the name of elements of quasigroup or loop <Q> to <name>
+##  Sets the elmNamePrefix property on the family of a Represntative of 
+##  collection <C>. For quasigroups, loops, and possibly related structures
+##  this changes the prefix with which the elements of that family are printed.
 
-InstallMethod( SetQuasigroupElmName, "for quasigroup and string",
-    [ IsQuasigroup, IsString ],
+InstallMethod( SpecifyElmNamePrefix, "for collection and string",
+    [ IsCollection, IsString ],
 function( Q, name )
     local F;
-    F := FamilyObj( Elements( Q )[ 1 ] );
-    F!.names := name;
+    F := FamilyObj( Representative( Q ) );
+    F!.elmNamePrefix := name;
 end);
 
 #############################################################################