It may have something to do with traditional values of Japanese Politeness. As detailed in Yamamoto Tsumetomo's Hagakure: Book of the Samurai, it is considered rude to remain silent when spoken to by a master, or when someone you respect does something worthwhile. Saying something, even if it's only their name, acknowledges that you understand, or that what they said or did has meaning to you.
This is very common, and is Truth in Television. After all, if there's more than one person around, simply saying, "Yoo-hoo" or "Come here" might cause confusion. Often done with an inflection that either extends the name into two syllables ("MA-ay!"), rises on the first syllable and falls on the second ("SI-mon!"), or rises on the second ("E-LI-za!") or third ("A-ri-AD-ne!") syllables depending on how many syllables the name has. As a general rule, the rising inflection is put on the second-to-last syllable. If the person is calling another person and using their first and last name, often the last name has the inflection ("A-de-line-FORR-es-ter!"). If someone is calling someone and is not sure if the other person is even there, they might instead use an inflection that is similar to the one used when asking a question ("Michael?!").
Getting their attention
Similar to calling someone, except they're there, just asleep, lost in thought, about to do something dangerous, or you want to start a conversation. If they're asleep or lost in thought, it's common for the person saying the name to say it first in a questioning voice, then if that doesn't work, in a shout, or possibly starting with saying the first name, then the first and last names in a questioning voice, then shouting the full name, usually with a message such as "get your head out of the clouds" or "wake up" attached. (e.g.: "Andy? Andy Smith? Andy William Smith, go back down to Earth right now!") If they're about to do something dangerous, the name is usually said loudly (but not generally in a different pitch) and quickly. This is also Truth in Television.
Inviting them to sing
Common when someone is doing a musical number. For example, if Brian is singing a song, then shouts, "Amy!", that means it's Amy's turn to start singing. Whenever this happens, the person whose name was said will nearly always know which lyrics to sing. However, this is generally only said when the person is inviting one person to sing. If it's more than one person, they'll generally say, "Now you!" instead and if it's everyone in the vicinity, they'll say, "Everybody!".
Being angry at them
Usually said in a voice that's either fast or slow, and occasionally the full name or the first name, middle initial/s, and last name will be used. Usually said by people in a position of authority (bosses, teachers, parents, principals, etc) and is a common way to scold pets, although it's not recommended with dogs: if you use a dog's name as a synonym for "no" too often, they might form a negative association with their name.
Being in love/infatuated with them
Quite often, people will say, "Oh, so-and-so" when thinking about their Love Interests or having an intimate time with them. When two characters are simultaneously developing romantic feelings for each other, they will often stare at each other and say each other's names, occasionally over and over.
Something bad happened to them
Quite often if someone is injured, seems out of sorts, passes out, dies, or suddenly falls into a dangerous or potentially dangerous situation, another person (normally a friend, lover, or family member) will say their name. If they're dead or dying, they might say their name a few times in a questioning way, then shout it when they realize that the person is dead/will die.
If someone dies, disappears, or goes away, their best friend, family member, or lover will often say their name in a wistful voice.
Noticing/being pleased to see them
Often (and this is Truth in Television), if someone notices somebody they will say their name and (usually) point, sounding more enthusiastic the more pleased they are to see them. If the person being noticed was previously in danger or mistaken for dead, this is another time an enthusiastic name shout is often in order.