That is a right pronounciation: though many in Punjab would pronounce it almost Dupindurr. The Sanskrit pronounciation was deependra coming from joining deepa (something that causes shine, i.e. that blazes, i.e. lamp or light) and indra (the king of the gods, the name is said to mean someone who can subdue, but possibly, the real connection is to dropping rain; the king of gods was originally the helpful god of weather, you see, with thunderbolt his weapon, he won against the demons and got the farmers' cows back to them). As an ending it often meant something like `the best of', or 'lord of', so it is the inder that you often see in Punjabi names. Thus, it can combine with jasu which derives from jas to weaken, or to strike, and similar terms were often applied to Indra's thunderbolt, or with guru, a word derived from the same origin as English gravity could mean not only heavy, but also a teacher. Just as an aside, I know little of the real etymology of Punjabi names: I can only guess from my knowledge of Sanskrit.
Anyway, the pronounciation of that that indra bit did not survive the ravages of time: the -a sound (short a like in run, not the long a ending feminine words) often went away. Well, very few Indian languages could pronounce a dr at the end and it became a der (and, yes, they often pronounce Louvre as Loovur) in some, others maintained the -a in cases like this.
The deepa bit has a long vowel, and unless stressed, those seem to disappear. In addition, when unstressed, palatal vowels like in hit often tend to get pulled back into the vowel in get, and then finally into the indeterminate form of the vowel in nut.
The -e- between the deep and ndra had come from combining an -a with an i-. But just as the ending -a of deepa went away like all ending -a's, the -e-, especially when stressed, became -i-.