That has nothing, except mispronounciation, to do with an h!
The word being asked for was dhAnyA, a Sanskrit word, and the word you are referring to is merely a form of the same word in modern Indian languages. Most Indians would write it as dhane/dhania (dhaniA in my notation) if they were writing in the roman script. The important point is that in many of the Indian languages, the sounds d and dh are phonemically distinct: dh is an aspirated version of d, not d followed by an h. In English, and many other languages of Europe, aspiration is rarely phonemic, and asprated voiced consonants like this are practically nonexistant. So, the mispronounciation of dhania as danya is common here, but practically nonexistant in the original language.
The word ultimately derives from dhA (cognate with English verb to do) meaning to hold or to bear: it referred to various seeds `borne by the Earth', but primarily to paddy (i.e. rice). Since rice was the staple food item in a large part of India, it became associated with lakSmI (the root meaning of this word is a mark or omen), the goddess of wealth. dhAnyA as coriander was just another meaning, and that survived in common speech as dhaniA.
Actually the story is slightly more complicated, there is a root dhan, to run, which gave rise to a lot of words meaning prize (in a competion) or wealth. In fact, a common word for `thank you' is dhanyavAda, which literally means `the speech of bestowing wealth' or something like that, basically, people are saying that you are great, that you bestow wealth. In any case, sometimes words with the same meaning appear both in the dhA- series and in the dhan- series. Thus dhanyA also means coriander, and also means great, literally bestower of wealth in the feminine. In fact, the cluster is probably even more tightly connected since dhan itself can mean to bear fruit, dhAnv to flow, dhAv means to run, and dhU to shake or agitate (the last with clear cognates in Greek).