There's a simple way to know the note names are how the sharps and flats are laid out. It's simple but let me see if I can explain it simply ;)

You WILL NEED to know those Intervals and the Cycle of Notes from my lesson info.

But

always start by writing down the notes, starting from your root, in order through the first octave. Say we want to learn the notes of the A Major scale. First write the Cycle of Notes starting on A trough the first octave...

A B C D E F G A

Now use the WWHWWWH Interval formula..

A is A,
a whole step from A is B...so B is B,
a whole step from B is...C#
a half step from C# is D
a whole step from D is E
a whole step from E is F#
a whole step from F# is G#
a half step from G# is A

So, you have A B C# D E F# G# A

So by starting with the note written out you just add the sharps (of flats if needed) and you end up with one of every note and the correct enharmonic name for it...so you don't mix sharps and flats, and you don't double the letters.

Look at F Major...

1. F G A B C D E F cycle using each note in one octave
2. WWHWWWH Interval formula

F is F
a whole step from F is G
a whole step from G is A
a half step from A is Bb
a whole step from Bb is C
a whole step from C is D
a whole step from D is E
a half step from E is F

You would use Bb not A#. Because you DON'T want A AND A# in your scale.

So write the notes out, let them determine the closest note name, then fill in the sharps and flats as you go through the cycle of notes.

This will also keep you in line with your Key Signatures stated in the Cycles of Fifths.

Read that link I posted, it'll help.