I'm pretty sure the name of this throw is called Ippon Seoi Nage. It looks like this: I would say that it is fairly simple and it was one of the first ones I learned. It happens when someone takes your back from standing and you throw them over your shoulder using a two-on-one grip on their arm. Since it is such a powerful throw, I would really like to use it in competition (BJJ, not Judo), but I'm not sure whether or not it's worth giving up my back for. What if it fails?
You do not purposefully give your back. You do not "give" anything. Applied correctly, your back is safe. There are some misconceptions here.
You do not simply "give your back". Throwing is something you should only do when you are in control of your own and your opponent's balance. It is fast, it is powerful, and it may well break your opponent's hip when thrown on concrete. It is hard to impossible to hook in when this throw is executed fast and low with an upright posture (hip low against opponent's thighs or drop version).
Since we are not speaking about Judo but BJJ, you should totally control the inside of your opponent's arm, may it be as per gripping into the crook of the arm (gi) or overhooking (no gi). This means that there is no way for your opponent to choke you right away.
Something most people forget is that this throw should involve some level of control of the "free" arm of the opponent in competition (see also 4.). Obviously not during the execution, but beforehand: if it is pushed away or pulled across just before the entrance, it is immeasurably harder for them to cling to you with their free hand and pull you around.
You can modify the execution and throw a morote seoi nage instead. This gives you more control over both sides of your opponent.
There are some pages on the internet that go over how to apply a shoulder throw in BJJ without your back being taken:
DO NOT GIVE UP YOUR BACK. Not only is this bad habit in competition, but this can become a bad habit in the case of a real altercation, which could cause serious harm. In competition, as the other answers illustrate, you are very susceptible to a rear-naked choke, and if you would ever develop a habit of that in a real fight situation, you could be hit with a blunt object, knife, etc.
Obviously you need to drill the technique, in case you end up in a bad position, just don't purposely put yourself there.
You absolutely should NOT give up your back in attempt to bait someone into getting in position for a shoulder throw (seoi nage, in judo terms). A competent opponent will break your balance while they are behind you, put you on the ground, and then apply a rear-naked choke (hadaka jime). If your balance is broken, you will not be able to throw.
If you want to throw someone, you need to put yourself in an advantageous position and your opponent in a disadvantageous position. This means that when you turn your back to throw them, you should have put them off-balance; you cannot expect your opponent to helpfully jump on your back after you turn.
I went to a Judo seminar 6 years ago where one of the instructors encouraged me to give up turning 180° when doing hip/shoulder throws. I now do them turning 90°.
This is the entry I use for Seoi Nage. On shorter people, I turn that into O Soto Gari.
I'll teach people the classic entries for hip/shoulder throws, but I will have them drill these alternate entries.
I'll add that if you can find someone skilled in Judo to teach you Seoi Nage, ask them to help you.