The dog used to be dubbed as Tebu though his real name was Tebukuro.
"その犬はてぶというあだ名で親しまれていた"
~していたものだ used to ~
あだ名をつける、称する dub, ここでは受け身で be dubbed
~として as
be dubbed as ~
~にもかかわらず though (接続詞)
The dog used to be dubbed as Tebu though his real name was Tebukuro.