I've heard moin for want why is eisiau being used?
Just like English has different dialects that use different words (e.g. "flashlight" in the US for "torch" in the UK), so does Welsh.
So you will hear both dw i'n moyn (or variations thereon such as wi'n moyn) more in the south, while dw i eisiau may be heard more widely (in the north, often in the form dw i isio, which is sometimes seen in writing like that as well).
They're both good Welsh. Use whichever one you like but be prepared to encounter the other one.
(Note the difference in grammar, though: dw i'n moyn versus dw i eisiau without yn.)