Within the four-level stack hierarchy, MoStacks uses names to identify backgrounds, cards, fields/controls and sort keys. The most important names are probably card names; beside this chapter here about general aspects of names there is a special chapter Card Names.
MoStacks handles names in a rather liberal way: They can have any "reasonable" length and contain most characters, not only letters and digits. E.g. a background name Special Cards, Group #1 is perfectly ok. Empty names are not allowed, however.
Internally, with few exceptions like card names in wiki texts, combo box card lists or scripts, MoStacks does not use names, but id numbers, to identify everything. This allows it to deal with situations where more than one object of a given kind as the same name.
For all the kinds of names discussed here, duplicate names are indeed allowed and (mostly) handled correctly. To enforce complete uniqueness for all names would be technically costly anyway and sometimes rather limiting for you as a user.
However, it is still a very good idea to avoid all duplicate names that are not necessary, because they have a great potential to confuse you when using the stack, and MoStacks helps you to keep them unique with some warnings/confirmations.