I want to preface this by saying, I only have a basic understanding of Hebrew. El does indeed mean "God". According to this site, Daniel means "God is my judge" and Dinah means "judged". With this in mind, dn or dnh would mean "judge" "judgement" or "judged". Vowels are filled in during transcription. Daniel then, would literally mean "God judge" "God judgement" or "God judged". I believe the "is my" part of "God is my judge" has been added in for clarification of the meaning behind the two parts of the name. I have also heard of Daniel meaning "Judgement of God" and "Judged by God", which would support the theory of adding in words to clarify a meaning.
ETA: I like wikipedia a lot, but it can't always be counted on for completely accurate information.
"It's the job that is never started that takes the longest to finish." - J.R.R. Tolkien