Sharke,
Sounds like you have a good baseline in knowing the shapes. That is the hard part IMHO. The naming is something that is not necessarily consistent across the board. For example, I had a number of music teachers who told me there was no such chord as a m7b5. If you analyze the m7b5 chord you will note that it is actually a m6 chord, however, in many instances the chord can be behaving like a II, V progression. i.e. B, A, D, F is a Dm6 chord with the 6th in the root. The same notes could be called Bm7b5, and I would actually call it Bm7b5 if the progression were Bm7b5 to E7 to Amaj7 as the chords are leading to the tonic, A.....II, V, I. In many cases naming conventions are not consistent, or, they are reflecting of the current key. For example, would you call G, A, D, F#, a D/G chord or a Gmaj7 add 9? Either works, and somewhat depends on the key or the knowledge of the player.
In your example of knowing a b13 not in the key of Eb, I would call that B, or the sharp 5th of the Eb scale... Knowing the shapes already can help you immensely in quickly identifying notes and the similarities between chords. i.e. m6 and 9 chords are similar. B, G#, D, F# = Bm6. Change the root to E instead of B and you have E9.
Here is how I think about naming in the context of Chords and some colorful examples in key of D using common guitar chord layouts...
Add 2/9 = Major chord with it's 2nd included. i.e. D2 or D add 9 = D, A, D, E
9th Chord includes b7 and 2/9 (7+2 = 9) i.e. D, F#, C, E
b9 or #9 includes b7 and b2/9 or #2/9 i.e. D, F#, C, Eb or D, F#, C, F
1tth Chord includes 4 and b7 (4+7=11) i.e. D, C, E, G
13th chord = 6, b7 (6+7=13) i.e. D, C, F#, B
13thb9 or 13th#9 = 6, b7 and b2/9 or #2/9 i.e. D, C, F#, B, Eb or D,C,F#,B, F
b13 is actually the same as Aug 5th. i.e. D, C, F#, Bb
There are many more possibilities but these are the general guidelines that I use. Hope this was useful, and not too confusing. The key is find a system that works for you.
Regards