Hi Caryn,
The present code truncates the site title at 96 characters, and removes any characters except for any in : A-Z, a-z, 0-9 and underscore, and replace spaces with underscores.
It seems that 96 is too many, at least for you - in the next release I've cut it to 32 - that ought to be enough to identify the site the backups are from!
The existing version already allows you to change the name with a filter... so, you have two options:
1) Update to the development version, which cuts it at 32 characters: http://updraftplus.com/faqs/devversion
2) Or, stay on the current version and create a filter, by creating a file wp-content/mu-plugins/cut-ud-name.php with contents (changing my_custom_name - but make sure it also obeys the above rules):
<?php
add_filter('updraftplus_blog_name', 'custom_updraftplus_blog_name');
function custom_updraftplus_blog_name() { return "my_custom_name"; }David