Is there any significance documented regarding his last name in light of the fact that "Kirk" means "Church"?
To the best of my knowledge, no. This was never brought up in TOS, it's not been mentioned in any documentary I've seen, and I haven't found a single reference to that factoid in any interviews with cast or crew.
Also, by the time of Kirk's birth in the ST Universe, English (US) was apparently the default language of everyone. Other languages (especially sub-dialects like Scottish-English) were retained in a purely local sense, if at all.
Kirk's family was primarily North American, with any European roots being multiple generations back. He was Iowa born and bred, and was almost certainly unaware of that factiod himself.
Out of Universe, the name 'Kirk' was chosen becasue it was similar to Captain Cook, an inspiration for the character.
People believe that Kirk word comes from Greek word "Kuriakon" but I think Turkish word "Kırk" is already totally fit and there is a Turkish country called "Kirkız" means We are Kirk , as Kirk is the most holiest word in Turks , Kirk=40 in Turkish and 40=forty in English ,Fortifying means to strengthen Castles on behalf of central authority , and every Turk be fortified being washed by water having 40 stones in and blessings at the 40th day of his/her birth .