Fatal error: Cannot redeclare THEMENAME_preprocess_page() In D7, we have two copies of the same Bootstrap Agency base theme modified to show on different URLs using ThemeKey.

This works, but whenever a new module is installed, the site crashes and we see the following in the Apache error log:

PHP Fatal error:  Cannot redeclare bootstrap_agency_preprocess_page() (previously declared in /sites/all/themes/bootstrap_agency_minimal/template.php:13) in /sites/all/themes/bootstrap_agency/template.php on line 13  

This is actually a very similar issue to this , I just couldn't comment on the above and Clive's answer wasn't all that clear to me. Is it better to merge the two functions or rename one of them - as the 2nd answer suggests? And what does merging entail?
Function names in template.php have to be prefixed with themename_function. At the same time, you cannot have a function declared twice.

bootstrap_agency_preprocess_page() should exist once in bootstrap_agency/template.php, and the other should be bootstrap_agency_minimal_preprocess_page() in bootstrap_agency_minimal/template.php.

If you do not need to do any override, and the one theme is a subtheme, you can simply omit it from template.php. Otherwise, you would need to copy the function code in and amend what you need to amend.