I think the Rabbit name was chosen more because rabbit can be used as slang for talk and chatter, you might say some people were “rabitting away together” and so on if they were conversing at length[1]. In the UK most portable TVs used halo type antennas for reception AFAIk, this might be related to the UK only using UHF for 625 line colour TV (and digital)[2] whilst the US also uses VHF. The main living room TV was / is usually fed from a roof mounted yagi antenna though.

[1] Just don’t use the phase “at it like rabbits” to mean conversations. Unless you mean Ugandan discussions… [2] VHF was used for the old 405 line system, which was turned off in the ‘80s.

Isn't the term "rabbit ears" more of an American thing? Can't recall anyone using it in the UK.