I think you will find that Matthew Kirkland Walker, was most probaly named after the Reverend Matthew Kirkland, who was appointed as Minister, of New Cumnock, Ayr. in 1835.
You can Google, Matthew Kirklands, name and you will find a History of the man.
In short he broke away from the established Church of Scotland, and started a Free Church, in New Cumnock, Ayr. and accordingly most of the parishioners followed him.
Alas after building the first Free Church, in New Cumnock, and a Manse, Matthew Kirkland, died 1846. in New Cumnock, where there is a large Memorial, dedicated to him.
As there is no apparent connection of the surname Kirkland, in your family then i am almost certain this is where the name came from.