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nirmala definitely means clean from the privative prefix nir (meaning out of or away from except when applied to words with a negative sense) applied to the word mala which meant dust, dirt, or physical or moral impurity and is found in the Atharvaveda already and cognate with similar sounding roots in other Indoeuropean languages like Greek and Latin.

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Nimmi is definitely a name used by the Hindi and Punjabi speaking population of Punjab-Delhi-UP region.

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What I do not know is whether the very plausible theory that Nimmi is the short form of Nirmala is actually correct. Since in India the pet forms of names are not necessarily shortened versions of the formal name (or derived from them by analogy), it is difficult to check it directly.