I have a few documents and templates that I've "Saved As" a few times. Whenever I open them in InDesign, they keep opening as Untitled-1.
How do I save these so that open as if they were already saved? This isn't happening with all of my files.
It is because you have saved them as InDesign templates (indt), not InDesign documents (indd). InDesign templates open always as Untitled-1 (except if you check the “open original” radio button).
But anyway, if you want to save them as InDesign documents, you will need to save them “as”
Oh, okay. Is that just how it works with templates? It was intentional to save them as templates, not documents.
Yes. InDesign always opens copies of .indt files so that you don't advertently overwrite the template.
You can quickly convert documents to templates and vice versa by just changing the extension (which changes the opening behavior, so changing .indt to .indd will put you at risk of overwriting). You don't have to open the file and save as with the new extension.
You can also update templates directly by just selecting .indt as the save type and accepting the overwrite of the existing file.
But yes, as in nearly all document apps I know, the only difference between a live doc file and a template is the extension (.indd/indt, .doc/.dot, .docx/.dotx).