I think he more than deserves it, he played Key role in Conspiracy against Yonkou. Might also have gotten more boost, given how big a raise Luffy got or how strong Sanji is. Bt all that dont matter because Vinsmoke name was mentioned,
If we are being technical, i think only 50 m part is Judge contribution as hinted by Reiju own words. She says that they elevated his bounty and changed it to Only Alive. Accepting they played a role in influencimg his bounty. Now since all members of SH got 50 m boost, it's fair to assume Sanji atleast would have gotten that as well, which only leaves 50m that Judge could have influenced.
I will concede to these 50m being increased due to Judge influence bt it still should be noted Sanji had done good feats upto DR to deserve his 177 m bounty. First being easily one shotting a Pacifista that rookies with good bounties couldn't do shit against, all in front of Marines who noted how Strong SHs have become Post ts. Sanji then beat Wadastumi in FI arc alongside Jinbei who has 400+ m bounty, infact he finished him off. And in PH again, he is one of few that fought, beat Caesar henchmens and saved the Marines from Vergo, again noted by Smoker unit. If each of SH can get 50m boost, Sanji who is part of SHs main fighting force getting 100m shouldn't be even questioned, bt here we are. 177 m bounty for some one of his strength was still underwhelming when Usopp even got 200m bounty.
As for his bounty after WCI island arc, his name yes could have contributed it somewhat. Let's go into this bit in detail. If family name could influence bounty that much, i want to see your case of Luffy getting boost pre ts, when his family name is in fact most dangerous in Onepiece. Dragon, Luffy father is the Most Wanted Criminal and Luffy is also grandson of Garp, the Hero who can rival Roger itself. Bt it never was the case, which make Sanji case clear as well. Suggesting it simply was a Gag based on Sanji fear that his family name might have contributed in his bounty bt that really was not the case in actuality and it was his key role as the Groom at Tea Party who messed up n decieved BM creating an opportunity to take her down. Him keeping up with Monsters in BM crew could have also been the reason for this bounty.