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From Elxis Official Documentation

Elxis uses a smart mechanism to auto select the proper translation of modules titles depending on user selected language. Modules installed by elxis default installation are published for all languages, in that case module's title pulled out from the corresponding php file for each language and any title provided by user is ignored.
In order to use your own title and overlap the default behavior you have to publish the module to one or more languages at the same time... but not use all languages option.

You can make copies of the module and publish one for each language with desired title.
Or you can change the title and publish this single module to the languages you want by selecting them one-by-one(not all languages option) in the dropdown box at module's configuration page.