What is the common name for brackets, braces, and parentheses?

I need to name a variable containing ()[]{}, what is the common name for all of them?

Two side questions:

• parentheses is plural, or singular, or both?
• is abbreviating it as parens understandable?

There isn't really an established generic for them; if I had to say something, I'd probably say enclosing glyphs. Trying to use "bracket" as a generic doesn't really work because "brackets" usually specifically means () in British English and [] in American English.

Seeing that you're naming a variable, I would probably go with $enclosures.

Parentheses is a plural; the singular is parenthesis.

"Parens" is usual and understandable, yes.

You can call all of them braces or call all of them brackets.

I have heard

• [] called brackets, square brackets, and square braces;
• {} called braces, curly braces, and curly brackets.
• () called parentheses

While it's true I have never heard () referred to as "curved braces" or "curved brackets" or anything like that, it is fine to lump them in with other "enclosing punctuation" as other answers and comments suggest.

I specifically recommend against enclosing glyphs because it is a little too snooty, as if you're some kind of English show-off trying to talk to programmers about programming. I don't mind calling these symbols enclosures, though in programming contexts, this term might be a little too close to closures, which are something else.

Don't forget that <> are also common enclosures, referred to as angle brackets or angle braces.

Finally, so that this answer addresses everything asked, I'll reiterate that () are parentheses; one of them is a parenthesis; and that these can be freely shortened to parens and paren, respectively, especially when talking to programmers.