Both Irish and Scottish Gaelic are derived from Old Irish but are considered separate languages today. Some refer to Irish as 'Gaelic' especially overseas. For clarity they can be called 'Irish Gaelic' and 'Scottish Gaelic'.
Kim is a foreign name, not Irish. So, an irish speaker would just use Kim. By the way, we don't call it Gaelic in Ireland. If speaking in the English language, it's called Irish (or the Irish language). If you're speaking Irish, it's called Gaeilge. In Ireland, Gaelic usually means Scots Gaelic.