Using Hack addon, I did a script to find teams using its name. I have thousands of teams, so it's really needed some kind of search method, instead to expend minutes searching for them while scrolling, scrolling...

How it works:
It adds a small, non intrusive EditBox in top of the label "Selected Team". Just move your mouse to it and you will see some fade effect. Click it, type your team name and hit ENTER. If there is any team matching its name with you typed, it will be selected. If you have more than one team matching, just hit ENTER again to select the next matched team.

I'm newbie while programming wow addons, so sorry for my mess in the code. Fell free to use or non use it in the official code, as you want.

The code:
local tm = LibStub("AceAddon-3.0"):GetAddon("PetBattleTeams"):GetModule("TeamManager");

FixPetTeams = FixPetTeams or tm;

function FixPetTeams:GetPetInfoBySpeciesIDLevel(reqSpecieID, reqLevel)
   local numPets, _ = C_PetJournal.GetNumPets();
   for idxPet=1, numPets do
      local petID, speciesID, _, _, level, _, _, name = C_PetJournal.GetPetInfoByIndex(idxPet);
      if (reqSpecieID == speciesID) and (level == reqLevel) then
         return petID, name;
      end
   end      
end

-- To use this function, just call: FixPetTeams:fixPetID();
function FixPetTeams:fixPetID()
   local PETS_PER_TEAM = 3;   
   local numTeams = self:GetNumTeams()
   
   for team=1,numTeams do
      for petIndex = 1, PETS_PER_TEAM do
         local petSlotInfo = self.teams[team][petIndex];
         local speciesID = petSlotInfo.speciesID
         if speciesID then
            local petID, name = self:GetPetInfoBySpeciesIDLevel(speciesID, 25);
            if petID then
               petSlotInfo.petID = petID;
               petSlotInfo.name = name;
               print( name );               
            end
         end
      end   
   end
end

-- --------------------------------------------- --
--    Adds support to search teams by name.
--

local GUI = LibStub("AceAddon-3.0"):GetAddon("PetBattleTeams"):GetModule("GUI");
FixPetTeams.GUI = GUI;

local widget = PetBattleTeamFrame;

function FixPetTeams:findTeamByName(nameFilter)
   if (not nameFilter) then return end
   
   local numTeams = self:GetNumTeams();
   
   nameFilter = strlower( tostring(nameFilter) );
   
   if (strlen(nameFilter) < 1) then return end
   
   local result = {};
   
   for idxTeam=1,numTeams do
      local teamInfo = self.teams[idxTeam];
      local sName = teamInfo.name;
      if (sName) then
         sName = strlower(sName);         
         local posName = strfind(sName, nameFilter, 1, true);
         if (posName) then
            --print( teamInfo.name );
            result[idxTeam] = teamInfo;
         end         
      end      
   end   
   
   return result;
end

--  To use, just call:
--      FixPetTeams.GUI:addSearchSupport()
--  Just for convenience (or lazy people like me - mwb):
--        
function GUI:addSearchSupport()
   local findTeamEdit = widget.findTeamEdit or CreateFrame("EditBox", "FindTeamEdit", widget, "InputBoxTemplate");
   widget.findTeamEdit = findTeamEdit;
   _G.findTeamEdit = findTeamEdit;
   findTeamEdit:SetPoint("TOP", widget, "BOTTOM");
   findTeamEdit:SetAutoFocus(false);
   --findTeamEdit:SetAllPoints();
   findTeamEdit:Show();      
   
   return widget;
end

local function findTeamEdit_OnTextChanged(self)
   local sNameFilter = self:GetText();
   
   local resultFound = FixPetTeams:findTeamByName(sNameFilter);
   if not resultFound then
      print("-----------------------------");
      return;
   end
   
   for idxTeam, teamInfo in ipairs(resultFound) do
      print( sNameFilter );
   end   
end

local function findTeamEdit_OnEnterPressed(self)
   local sNameFilter = self:GetText();
   
   print("");
   print("-----------------------------");
   
   local resultFound = FixPetTeams:findTeamByName(sNameFilter);
   if not resultFound then
      return;
   end   
   
   local idxCurTeam = FixPetTeams:GetSelected() or 0;
   local idxNewTeam = 0;   
   local idxFirstTeam = 0;
   
   for idxTeam, teamInfo in pairs(resultFound) do    
      print( "#" .. idxTeam .. " " .. teamInfo.name );      
      
      if (idxFirstTeam<1) then
         idxFirstTeam = idxTeam;
      end
      
      --print( idxTeam );      
      if (idxTeam > idxCurTeam) then
         if (idxNewTeam==0 or idxNewTeam>idxTeam) then
            idxNewTeam = idxTeam;
         end         
      end   
   end
   
   
   if (idxNewTeam<1) then       
      idxNewTeam = idxFirstTeam;
   end
   
   --GUI:ResetScrollBar();     
   --PetBattleTeamsScrollFrame:Hide();
   FixPetTeams:SetSelected(idxNewTeam);
   --PetBattleTeamsScrollFrame:Show();
   
   do
      local self = PetBattleTeamsRosterFrame;
      local teamFrames = self.scrollChild.teamFrames
      local rowHeight = teamFrames[1]:GetHeight();
      
      local totalHeight = self.scrollFrame:GetVerticalScrollRange()
      local tot = totalHeight;
      local pos = tot / (rowHeight+64) * (idxNewTeam-1);      
      if (pos<0) then
         pos = 0;
      elseif  (pos>tot) then
         pos = tot;
      end      
      self.scrollFrame:SetVerticalScroll(pos)          
   end   
   
   print( "TIME: " .. idxNewTeam);   
end

local FIND_EDIT_GAIN_FOCUS_ALPHA = 0.95;
local FIND_EDIT_LOST_FOCUS_ALPHA = 0.3;

GUI:addSearchSupport();

widget:Hide();
findTeamEdit:Hide();
findTeamEdit:SetFrameStrata("DIALOG");
findTeamEdit:SetAlpha(FIND_EDIT_LOST_FOCUS_ALPHA);
--findTeamEdit:ClearAllPoints();
findTeamEdit:SetAllPoints(widget.selectedTeamText
--findTeamEdit:SetSize(60, 25);
--findTeamEdit:SetPoint("TOP", widget.selectedTeamText "BOTTOM");
findTeamEdit:SetScript("OnTextChanged", findTeamEdit_OnTextChanged);
findTeamEdit:SetScript("OnEnterPressed", findTeamEdit_OnEnterPressed);
findTeamEdit:SetScript("OnEnter", function(self)
      widget.selectedTeamText:SetAlpha(FIND_EDIT_LOST_FOCUS_ALPHA)
end);
findTeamEdit:SetScript("OnLeave", function(self)
      if (strlen(self:GetText())==0) then
         widget.selectedTeamText:SetAlpha(FIND_EDIT_GAIN_FOCUS_ALPHA)
      end      
end);
findTeamEdit:SetScript("OnEditFocusGained", function(self)
      self:SetAlpha(FIND_EDIT_GAIN_FOCUS_ALPHA);            
      widget.selectedTeamText:SetAlpha(FIND_EDIT_LOST_FOCUS_ALPHA)          
end);
findTeamEdit:SetScript("OnEditFocusLost", function(self)
      self:SetAlpha(FIND_EDIT_LOST_FOCUS_ALPHA);      
      widget.selectedTeamText:SetAlpha(FIND_EDIT_GAIN_FOCUS_ALPHA)
end);
--findTeamEdit:SetScript("OnEscapePressed", function(self) self:SetText("" end);
findTeamEdit:Show();
widget:Show();