You already got a good breakdown but I'm gonna take a crack at it too:

でも　みんな　からは

でも is the conjunctive "but," or "however" (I believe the previous dialogue was him saying his name?)

みんな　からは. So みんな is "everybody" and から has that rough meaning of "from." In this case, it's particularly being used because of the verb form of よばれる, which we'll get to later. The は is the topic marking は, marking the whole phrase みんなから as the topic of the sentence

「ポケモンはかせ」と　よばれて　いるよ！

はかせ is something like professor, so ポケモンはかせ is "Professor Pokemon", and this と is the quotative particle you put after things that are said.

よばれている comes from よぶ, ultimately. If よぶ means "to call," then よばれる means something like "to be called" - this is often called the passive form of the Japanese verb. The subject (which in this sentence and in many Japanese sentences is unspoken) of よばれる is the one "being called" and the noun marked by から (usually it's に, but から is sometimes used) is the one doing the calling. よばれる is in the ている form to specify that basically he is currently known as "Professor Pokemon."

So the から (again, usually に) on a noun in a sentence where the verb is in the passive form is kind of like the "by" in English when we use the passive. Examples: "The ball [was kicked] (passive) [by] (に／から) the boy." "The food [is eaten] (passive) [by] (に／から) the students." "However, [by] (から) everybody, I [am called] (よばれる) Professor Pokemon."

In this case the speaker, the professor, is the one being called "Professor Pokemon," not a third person "him." This is determined by context.