Should I change text-domain of TGM library inside theme?

Themes should always have only one textdomain – most of the localization tools base on that assumption, so if you put multiple textdomains in the same theme, you make localizing it much harder.

As for wordpress.org… It is clearly stated that:

Themes that are hosted on WordPress.org the text domain must match the
slug of your theme URL (wordpress.org/themes/). This is needed
so that the translations from translate.wordpress.org work correctly.

The text domain name must use dashes and not underscores and be
lowercase. For example, if the theme’s name My Theme is defined in the
style.css or it is contained in a folder called my-theme the text
domain should be my-theme.

The text domain is used in three different places:

In the style.css theme header As an argument in the localization
functions As an argument when loading the translations using
load_theme_textdomain() or load_child_theme_textdomain() style.css
theme header #style.css theme header The text domain is added to the
style.css header so that the theme meta-data like the description can
be translated even when the theme is not enabled. The text domain
should be same as the one used when loading the text domain.

Source: https://developer.wordpress.org/themes/functionality/internationalization/#text-domain

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