If you already have an international version of Vegas Pro, you can change the language directly instead of repurchasing it from a Korean agent. An easy way is to use the SeMW Extensions, where you can directly modify the language of Vegas Pro. Another way is to modify the registry manually, which can be cumbersome for some people.
I don't think the English installer includes Korean these days. Did you purchase the software from a Korean vendor? I'd contact support- maybe you can get a refund and buy one for your region instead.
Update: I was wrong, the SeMW extensions don't seem to be able to modify the language of the higher versions of Vegas Pro. You can only modify the registry manually.
For modern versions, you can use Notepad to create a new file and write the following text, save as a .reg file, and run:
Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SOFTWARE\VEGAS Creative Software\VEGAS Pro\21.0\Lang]
"ULangID"=dword:00000412
[HKEY_LOCAL_MACHINE\SOFTWARE\VEGAS Creative Software\VEGAS Creative Software Video Plug-In Pack\1.0\Lang]
"ULangID"=dword:00000412
[HKEY_LOCAL_MACHINE\SOFTWARE\VEGAS Creative Software\VEGAS Creative Software OFX GPU Video Plug-in Pack\1.0\Lang]
"ULangID"=dword:00000412
[HKEY_LOCAL_MACHINE\SOFTWARE\VEGAS Creative Software\Error Reporting Client\1.0\Lang]
"ULangID"=dword:00000412
For VP19 and earlier versions:
Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SOFTWARE\Sony Creative Software\VEGAS Pro\19.0\Lang]
"ULangID"=dword:00000412
[HKEY_LOCAL_MACHINE\SOFTWARE\Sony Creative Software\VEGAS Creative Software Video Plug-In Pack\1.0\Lang]
"ULangID"=dword:00000412
[HKEY_LOCAL_MACHINE\SOFTWARE\Sony Creative Software\VEGAS Creative Software OFX GPU Video Plug-in Pack\1.0\Lang]
"ULangID"=dword:00000412
[HKEY_LOCAL_MACHINE\SOFTWARE\Sony Creative Software\Error Reporting Client\1.0\Lang]
"ULangID"=dword:00000412