Not every group of notes has a name, but with most you can put together some name. Your first unknown E, F#, and G# can be looked at an Eadd9 (thanks Charles). Your last example B, C#, and F# is just a Bsus2.
A chord is technically any set of 3 or more notes so technically any group of 3 or more notes is a chord regardless if it seems to be missing notes or not. Most chords are nameable and all set of notes can be reduced to a prime form which is a very computational way of looking at chords.
To name chords based on notes can sometimes be tricky especially since some groups of notes yield multiple chord names, but there are ways to look at groups of notes to see what chords they make. Here are a few things to remember when looking at groups of notes to name chords:
- The bass note is not always the root of the chord.
- Chords are typically built in 3rds, so try and stack the given notes in thirds.
- The 5th of a chord can typically be omitted.
A little trick I use when naming chords is to take the note I think is the root of the chord and compare it against the major scale with a lowered 7th (the Mixolydian mode). The reason I do this is because how common the dominant 7th chord is and how extentions typically line up very well with this scale. I'll show you with the examples givin.
EX1 - C# E G# B F#
We can see that the first 4 notes stack up nicely in 3rds so let's assume C# is the root. Now we compaire all the notes to the C# Mixolydian scale:
C# D# E# F# G# A# B
C# X E F# G# X B
As you can see we have a 3rd, 5th and 7th. The 3rd is lowered which is fine it just means the basic triad is minor. We don't have a 9th or a 13th, but we do an 11th. From this information we can call the chord a C#m11.
EX2 - E F# G#
We only have three notes in this chord and they are all next to each other step wise. We can guess that is E is the root and let's compare the notes to the E Mixolydian scale:
E F# G# A B C# D
E F# G# X X X X
As you can see we have a 3rd, but we are missing a 5th and 7th. Missing the 5th is not a big deal, but because there is no 7th any extensions need be considered "added". There is one extension a 9th so from this the chord is an Eadd9.
Will finish the others soon...