Naming amitriptyline by IUPAC
Note: As stated in a comment to the question by Loong, the preferred IUPAC name according to the 2013 nomenclature recommendations is:


  3-(10,11-dihydro-5H-dibenzo[a,d][7]annulen-5-ylidene)-N,N-dimethylpropan-1-amin‌​e


The only change this makes to the analysis it that we can ignore the ‘incorrect’ cycloheptene, because [7]annulen is automatically a cycloheptatriene-type molecule.



First, let’s separate the name into its fragments. We have:


3-something-propane-1-amine
N,N-dimethyl
(10,11-dihydro-something)
(something-5H-dibenzo[a,d]cycloheptene-something)
(something-5-ylidene)


I’m going to start with item 4, since that is the main bicycle. Cycloheptene sounds like this molecule:



But the [a,d] and the dibenzo is telling us that we have a fused polycyclic unsaturated hydrocarbon, so we will need to add two more double bonds. (Skipping a picture of this step.) Dibenzo means that there are two fused benzene rings, and the letters in square brackets symbolise the attachment points. a stands for 1,2; d for 4,5 (analogously for other letters). With that, we get a tricyclic compound with many double bonds. However, it is still ambiguous how exactly to place the double bonds, we need the information 5H — it tells us that the ‘additional’ hydrogen must be at the 5-position. Beware: The 5-position does not reference the initial numbering we used for fusing the rings; the atoms are renumbered according to the rules for aromatic polycycles: Starting at the top right and going clockwise, ignoring all bridgehead atoms. So we get 5H-dibenzo[a,d]cycloheptene which looks like this:



Next up, item 3: 10,11-dihydro. This means that the double bond in the seven-membered ring is hydrated, i.e. there is a single bond instead.



And finally, item 5: 5-ylidene. We are attaching something to carbon 5 via a double bond. We’ll get back to that.

Item 1: 3-something-propane-1-amine. That’s nice and simple, we’ll first consider propane-1-amine:



N,N-dimethyl (item 2) tells us that there are two methyl groups attached to the nitrogen, giving us the following:



And now we need to add the entire tricyclo-blurb to the propane’s 3-position using a double bond:



And voilà, there is amitriptylene!