When it comes to entity labels, there are no worries. However, take special care when choosing your ECK entity's 'machine name'. ECK will check to make sure no other entities with the same 'machine name' conflict before allowing you to create it; however, there are aspects that cannot be checked for.
There have been several reported cases of other conflicts happening. See #1345264: Incompatibility entity type with machine name "category". In this example an entity of type category was defined using ECK; however, the user module has a function called
user_category_load(). So, when the entity API tries to call the load hook for the category entity, it checks for all modules essentially calling a
hook_category_load which conflicts with the user modules completely separate use of that function name.
Another example is if I were to define an entity called user_profile, it would seem a valid entity name and, thus, would get created. However, again the user module has a template file
user-profile.tpl.php that requires certain variables and gets triggered on the path
/user-profile. The same path is used by default for the user_profile entity I created using ECK. This again results in a conflict and it all breaks down.