The name of this street comes from the Royal Family and in particular Prince Albert. "The name Saxe-Coburg-Gotha came into the British Royal Family in 1840 with the marriage of Queen Victoria to Prince Albert, son of Ernst, Duke of Saxe-Coburg & Gotha. Queen Victoria herself was the last monarch of the House of Hanover." (https://www.royal.uk/).
“That on the application of the owners, two new streets on their property situate off Roslyn Street and London Street be named ‘Gotha Street’ and ‘Coburg Street’.” (21st August 1895).