What does 遍 mean in 小编遍搜多名?
遍 means allover;everywhere here. 遍搜 means search allover/everywhere. Basically it has the same meaning with 搜遍, but with the 遍 being put ahead OP wanted to emphasize the degree of how many bloggers he checked.
多名 is not the abbreviation of 很多有名, but just 很多名, i.e. many. 名 is just the measure word of the people, i.e. 博主.
盆友 is a net slang, means 朋友.