If you are seeing that on the actual public facing web page, then you need to turn off debug mode on your live site. You should never be showing debug info to the public, as that can be a security risk. If you need to debug a live site, you should set it up to write to the debug.log file, instead of outputting errors/notices to the screen, and then disable debug mode when you are done with your testing/debugging.
Having said that, the message you indicated is simply a “notice”. It’s not an error, and it won’t cause any issues. The particular line of code is in a function another contributor added several years back to allow you to display only first name and last initial of the person who signed up on the front end (if you don’t check the options to either hide names, or to show the full name). So, it seems to me that somehow you managed to sign up someone for a task without entering a last name, as the code is not finding any text in the last name fields to create the last name initial for display.
It’s not going to break anything, but I would look at your database for that particular signup (signups are saved in the pta_sus_signups table) and see if that signup is actually missing a last name. If a person signed up directly on the front end via the signup form, it shouldn’t be possible, since first name and last name fields are both required. But, perhaps if you used the admin live search feature to signup an existing user that did not have a last name already saved in their user profile, that could cause the issue?
But, like I said, it’s just a notice, and won’t break anything… you just won’t see an initial for the last name displayed for that particular signup.