The article on the name Daniel at Wikipedia is indeed inaccurate.
DAN: This is the present participle of the verb DIN, to judge, vindicate: "judging", "he who judges" > "judge". (1)
I The "i" in the name Daniel consists of two characters in Hebrew script: YOD (a consonant) and HIRIQ (a vowel). A lot of times the two occur together as a unit representing the sound "ee". (This goes back to times when no vowels were written and consonants were inserted to clarify the pronunciation.) The HIRIQ compaginis appears in Hebrew poetry as a suffix at the end of a noun (or a participle). It is called compaginis because ist just goes along with the noun without changing its meaning (it may have had a meaning of its own, but that got lost). Now the HIRIQ compaginis looks exactly like the first person singular suffix used in ancient Hebrew (not in modern Hebrew as Wikipedia states; in modern Hebrew it has to a large extent been replaced by the possessive pronoun sheli, "of me"). Within a Hebrew text it is usually easy to tell one from the other, but in a name you just don't know, whether the "i" is the suffix "my" or the HIRIQ c.
EL The only part that seems to be clear.
Now the translation "God (my) judge" may be a little misleading. A better translation would be "God vindicates (me)." Barrenness was considered a great disgrace in biblical times and would lead to mockery and the question: What did that woman do wrong so that God punishes her? A child (preferably a boy) given by God would vindicate that woman, so God was her vindicator (judge) and she could say: God is my vindicator/judge. (2) From that personal statement there is only a short step to a more general statement: God vindicates. So both interpretations of the name Daniel make sense, and you can't tell which one is correct. Probably the more personal interpretation is the older one
(1) Theoretically it could also be "perfect tense": This can refer to an action in the past or a general statement (God has vindicated me / God vindicates) (In fact there are no "tenses" in our modern sense in biblical Hebrew - in modern Hebrew there are.) I would say, in this case, DAN cannot be "perfect tense", because these forms never go with either the possessive suffix "I" (in this case it would be daneni) or the Hiriq compaginis (this is what my grammar books say). However, the Encyclopedia Judaica obviously interprets DANIEL that way: "God has judged, or vindicated", so I am not quite sure.
This answer doesn't really match the level of the question, I am afraid. But there may be some people out there who are interested. Or others who know better. The Hebrew classes I taught date back a couple of years ...