1) Go into projectm>pf>system>common5.pac and open the file with Brawl Box.How exactly did you remove the names above each of the character selection icons? Did you just delete them or did you replace them with "invisible" name icons?
2) Go into sc_selcharacter_en and then to MiscData[30]
3) There you will find a tab that says "AnmChr", expand that.
4) Search for the file named "MenSelchrFaceI_TopN__0", expand that as well
5) Click on "nameEA7" and write -100 on Translation -> Y