[subject] + 以 + [noun] + (的) + 名义 + [verb phrase]
以…的名义 says whose name an action is carried out in – a person, a company, a group. The whole phrase goes before the verb. It's formal: contracts, letters, announcements, reports.
With a short noun, 的 is often dropped: 以个人名义, 以学校名义.
The same phrase can mean "under the pretext of": the name stated is a cover for something else. Only the context tells you which reading is meant.
English puts "in the name of" at the end of the sentence. The 以 phrase sits between the subject and the verb.
代表 is the plain verb "represent, on behalf of" and needs no frame: 我代表大家感谢王老师.