For most names, just google and you will find many, many links. But many of them will have completely made up meanings, and you will usually have no idea which ones (and, often all of them will agree on the same wrong meaning). So, please be ware.
Incidentally, what I found interesting is that when you found a number of meanings, you chose one as the most plausible? And, yet, it is obvious you do not speak the language (Sanskrit) from which the name is derived. Will you please explain how you chose that one (I do not know how to explain this, but this is not a sarcastic comment: I mean it as a serious question and really am interested in knowing how people decide these things.)
I have not seen niranjanna with a doubled -nn- like that. But, I have seen niranjana, which has a long open -a at the end (like in English car), and the -nj- has a palatal (soft) -n-. This is the Sanskrit word which you are describing here (as you point out, barring typos).
There is a very old Sanskrit root anj (with the same soft n), which means to anoint, and is cognate with lating ungo. The prefix nir-/nis- modifies meanings with a sense of out/away, and niranjana (with a short schwa -a at the end) literally means unpainted or pure. Niranjana with the long -a at the end is the feminine form of this adjective.
In Hindu mythology, one of the supreme deities, shiva, is considered dispassionate and without qualities, and niranjan also conveys this: passion and all qualities are considered anonintments on individuals. Durga, his consort, and the supreme unqualified power, is called niranjana (with a long -a) for the same reason. The time period of the full moon is also called niranjana (feminine), this time probably because the full moon is full. I have heard of a niranjana (feminine) river in a poem, but I do not know where it is.
The `free from falsehood' is probably someone's explanation of pure, and it is true that the two concepts are related in Hindu thought, but that is not a meaning. Anjan does not mean fear to my knowledge, in Sanskrit or any other Indian language, except to the extent that fear is an emotion and emotion is an attribute, and anjan (the word is actually anjana, but the last -a is dropped in many modern Indian pronunciations) does mean attribute as I stated above. anjan has been used in the sense of mAYA (which means illusion) because illusion is `painted on' or an anointment of reality; and in some schools of Hindu/Buddhist thought, all the feelings of self and belongings are considered illusions, and niranjan has been used in the sense of someone who has transcended these illusions. niranjan is indeed anjanasya abhavah (there is no -a at the end of that form) which literally means non-being (a-bhAva-h) of-anjana (anjana-sya) in Sanskrit, but that does not make niranjana a portmanteau word.