I'm writing a series that has to do with vampires. My middle name is Amara, and I personally find that name really, really pretty. I wanted to add it to my book as the name of the main character but I remembered that one of the dopplegangers in The Vampire Diaries is named Amara. I don't want to get into trouble or anything. Would it be okay to use that name since it's still a name that belongs to me personally, even if it was used in another book series/show?
There exist Harry Mason & Harry Potter both are Harry. We have similar fist names out there that can create an issue what you do not want to do is copy the exact name unless the character is free use/public domain.
If you are concerned you can ask a lawyer but I do not think two first names with the same spelling is the issue however it sounds like your real issue is can two Vampire books have characters who have the same first name? The issue being of similar type of works at face value in the sameway you can't have two retail stores that sell clothing named Jamie's Closet. I could however have a retail clothing store & a band both named that because they are not the same thing.
My example Harrys above is of a video game character the other began as a book character so they are technically different. Even after Harry Potter became a video game character there was no issue but this could also be time & genre Mason comes from horror while Harry is child adventure.
If you like play on the name you can try Omara, Omarra,Amarah, Amarra, Ahmara, Umarra. Marra, or Emarra for examples you can also just pair the first with a last name that is truly separate like Amara Stone or Amara Crossglow.
Keep in mind appearances if both women have black hair and the Vampire Dairies has long you might want to change the look of yours with short black hair or she has a streak of red in her hair or iconic earrings just to make sure Vampire Dairies can't come hit you with a lawsuit because they've found too many similarities between your Amara and their Amara.
Lawsuits have gone off because a gag version character is to similar (kind of the point to convey the gag) but on it's own I do not think two Amara's existing in Vampire fictions is a stand alone issue it's the other factors like look, powers, traits that up your chances of them being angry with you.
I use this example a lot because it touches on this when it deliberately was used, but I know of two characters who were named to deliberately invoke famous characters for humor or for background purposes.
The first is the Happy Day's character Ralph Malph (pronounced similar to Mouth). When discussed with the other characters, a recurring gag was that his father was Mickey Malph and his mother was Minnie Malph. The gag of course was that their names were very similar to Mickey and Minnie Mouse (Ralph and his parents were all portrayed as having a very broad sense of humor.) Here it was mostly used for a gag (Mickey Malph got further name-checked in a Simpsons episode, where he is listed as "an original character" just like Sherry Bobbins [Mary Poppins] and Monald Muck.)
On a more serious side, the Degrassi: The Next Generation character James Tiberius "JT" York shares a similar sounding name to Captain of the U.S.S. Enterprise James Tiberius Kirk (Tiberius being a rather unusual name most famously prior to Kirk used by a Roman Emperor who wasn't all that interesting). In the show, as is my understanding, it's explained that JT's parents were both Canadian nerds and named their kid after the sci-fi icon famously played by Canadian actor William Shatner. Here the similarities between the two characters begins and ends with the name. JT has very little personality wise in common with Captain Kirk, is an average teen in late 00s Canada, and is so embarrassed by the name he prefers people calling him JT over James or Jimmy.
In both cases the characters are different enough that there was no cause for concern over copyright and as said, names cannot be copyrighted.