Why was the first man called Adam? I have started reading the Bible and I have found that in Genesis 2.19 the first man is already called Adam without any previous reference to this name. 

But when it comes to Eve there is a clear explanation of her name in Genesis 3.20.

So my question is, how was Adam's name chosen? Was it chosen by himself or given to him by God? And why?

In case different traditions have different answer to this question I would prefer the Roman Catholic one.
'Āḏām comes from the Hebrew 'āḏām, meaning "human being, mankind collectively, cognate with Phoenician 'dm (probably adam), Arabic 'adam human being; further etymology uncertain: perhaps related to 'aḏamāh earth, ground (compare the juxtaposition of 'āḏām and 'aḏamāh in Genesis 2:7, where God forms man out of earth) or to 'aḏom red, ruddy" (OED).