1) Fictional cat 2) ITV sitcom 3) To move away 
[online music] MOG was a paid subscription online music service and blog network, where subscribers can listen to and read about music. Subscribers could play the tracks that were available in the catalog on a variety of digital devices, including computers, handheld devices, Sonos system and television. The company claims that its catalog ...
• (v. t.) To move away; to go off.
Mog transitive verb [ imperfect & past participle Mogged ; present participle & verbal noun Mogging .] [ Etym. unknown.] To move away; to go off. [ Prov. Eng. or Local, U. S.] 
Mog is British slang for a cat.
Mother of the Groom
Manual Of Guidance