Thanks for your quick reply Magnussoft!
I'm really surprised by how poorly designed the admin interface is. Should I really have to go through that ridiculous process to change something so basic? And why are there editable field in the properties dialogs for the individual Navigation Menu items if they're not editable that way?
Anyway: for others having this problem a more step-by-step explanation:
Go to "Builders > Navigation Menu" and find the item you want to change the text that your users see in the Navigation Menu of.
Click on that item and an "edit item" dialog will pop up. Highlight and copy the text in the "Language Key" field.
I didn't find Magnussoft's suggestion of doing the editing in "Administration > Settings > Languages" to be helpful - when I searched for the items using the really, really poorly-designed "Manage Keys" search field (if you type or paste something in it and hit your return/enter key on your keyboard it generates a PHP error message - you have to check the "apply" box instead") it wasn't returning the items I needed and the naming conventions were confusing.
I figured that directly editing the language file via FTP would be easier so I opened up the lang-en.php file inside the langs directory in my Dolphin install, and, after making a backup copy of it, used the search function to find the items I needed to edit. So for instance: the line for "Profile" has a language key like this: _Profile
I found that line in the lang-en.php file and it looked like this:
'_Profile' => 'Profile',
and I just changed it to this:
'_Profile' => 'My Profile',
and saved the file.
That's what worked for me - I hope it's helpful to others.