Sunflowers have perfect flowers with both male and female parts. So, yes, it should be self-pollinating. Titan is an heirloom; so, it should breed true, too, provided it isn't cross-pollinated by another breed.
There are said to be many flowers within each sunflower head. The first link I mentioned talks about how sunflowers protect themselves against inbreeding, but I don't know why that would be an issue anyway, if the plant is stabilized (unless it mutates or really wasn't stabilized). A stable plant shouldn't have any heterozygous traits that are important to the breed. Sunflowers are diploids, like many other plants (so, it shouldn't be as hard to stabilize them as it is for tetraploid plants). Alina may be able to add clarity to the inbreeding issue. I'm guessing the worry is about mutations, which could create heterozygous genes. Maybe sunflowers mutate a lot.
Here's an article on inbreeding, though. What I dislike about these articles/discussions is that recessive traits are often equated with deleterious traits. Recessive traits are very often good much as dominant traits are very often good. The only difference is that if a recessive trait is expressed, then the dominant trait has been bred out and shouldn't return, while if a dominant trait is expressed, then the recessive trait may or may not still be in the genetics. Mutations are said to be more commonly recessive, though; so, maybe that's what the whole thing is about.
If you just leave the plant alone, it should drop seeds that will sprout the next year. However, if you spread the seeds around in the fall/spring (if they're still attached to the head), you should get a lot more plants. Smaller sunflowers seem to drop seeds more easily, but Titan has large seeds/heads; so, you may need to remove them manually after the plant has died/dried.
Anyway, all that being said, I would still plant multiple plants, especially if what Alina says is true about more empty seeds being in self-pollinated plants, and if mutations are common enough to merit a concern about inbreeding. However, I'm guessing you'll still get enough seeds either way (you only need a few seeds to get a few plants), but, I say, the more the merrier.
If you were in charge of keeping the true variety alive, or if you were going to sell seeds labeled Titan, you should probably be concerned about inbreeding.