To start out, we'll get familiar with a system of politeness that we don't have in English. In English, we have "cuss words" or "curse words" that we're not supposed to use when talking to people who we're supposed to be polite to. These words can only be used (without insulting someone) when talking to peers in informal situations, or when insulting someone. The level, or register, of speech reserved for polite, formal situations or talking to someone above you in the hierarchy, is called "formal". The register of speech reserved for informal speech to peers or for insulting someone is called "informal". Sindarin doesn't have cussing, (beyond insulting names to call someone) so, the easiest way to insult someone in Sindarin is to use the wrong register when talking to someone.
If you're talking to a close friend, using the formal register will put distance between you and your friend, saying that you aren't friends anymore.
If you're talking to someone you're supposed to be polite to, like a superior or a stranger, and you use the informal register, you'll be dragging them to your level or below you, saying that you have no respect for them.
Using the informal register when talking to a friend puts them on your level, stating your closeness. When using it with inferiors, (students, employees, subjects that you rule over) it reinforces the hierarchy, and lets people know who's boss.
When you use the formal register with a stranger or someone above you in the hierarchy, it shows your respect for the person you're talking to, elevating them and putting a polite distance between them and yourself.
If you aren't certain how formal or informal you should be, err on the side of formal.
Like in many Indo-European languages, there's a formal "you" and an informal "you" in Sindarin. You can spot the formal "you" because it begins with an L, and the informal "you" begins with a C or G.
Example:
Se i chadhu gîn? - Is this (informal) your chair?
Se i chadhu lîn? - Is this (formal) your chair?
Like in English, Sindarin has a bunch of contracted forms, especially when it comes to pronouns. There's a bunch of possessive pronouns turned into suffixes onto nouns. A good rule of thumb is, "the longer it takes to say something, the more polite it is," which is how you can spot it.
Example:
Thíreg bain. - (informal) Your face is beautiful.
I thîr lîn bain. - (formal) Your face is beautiful.
Hadhathol? - Would you please sit?
Hadho! - Sit!
For Elves, their Father Name, the name based on one of their parent's names, is similar to a surname for us. In formal speech, you'd use this name to refer to someone.
The Elf's Mother Name, or Chosen Name will be very personal and important for the individual, because this name will have a meaning referring to some important part of the individual's personality and character. Using such a name would mark a very close, intimate relationship to the character, making this name for informal speech.
After Names are kinda like nicknames, but there are a few different kinds. If it's a flattering After Name that the character has adopted as one of their names, then it's fine for formal or informal speech. Unflattering After Names are better kept to informal speech.
For the example, let's look at Galadriel's names:
Artanis = Noble Woman (based on her father's name, Arafinwë, making it a Father Name, and thus formal)
Nerwen = Man Maiden (given to her by her mother because she as a maiden was as tall, strong, and fond of sports and hunting as a man. In Elven culture, hunting is a very masculine thing. It's a very personal name, and only for use in informal speech.)
Galadriel = Lady Garlanded with Radiance (very flattering After Name, she won't mind if a complete stranger uses this name for her)