I found a strategy called "covered combo" where you sell 1 put, 1 call, and purchase 100 shares of the underlying; is there a name for doing this without purchasing the 100 shares?
The strategy you are asking for is called straddle. To be more precise, as you would like to sell one put and one call option, it is a short straddle.
Both options are referring to the same underlying security, strike price and expiration date. Be aware that it is a very risky strategy, as gains are limited and losses are not restricted.
The wikipedia article mentions
The risk is virtually unlimited as large moves of the underlying security's price either up or down will cause losses proportional to the magnitude of the price move.
I called a straddle a "very risky strategy", which should be true for many (often less informed) private investors, handling around with option-strategies and thus using derivatives in a speculative way. As stated in the comments, a straddle (as any derivative) is also very useful for other purposes than speculating.