Change name on SSN Card after name split in Indian Passport?

Recently I split my name in passport. Now after the name is split do I have to notify social secutsec office and get a new card with my corrected name. Will my name change in the i94 form automatically?

What about the tax filing? Does the past taxes filed make any difference?

Do I have to notify TransUnion or credit karma regarding name split?

Government records Name changes

Name on Social security card is dependent on the name you have on your i94.
Your name on i94 is dependent on your visa.
Your visa name is based on your passport name.

So, you will have to get name change done at visa level first to match your passport. Whenever you apply for your visa extension next, your name should be matched with your passport name and hence new i94.
Once that is done, you can visit Social security office and apply for a new SS card with changed name.

Private company names changes (TransUnion / Credit karma)

They pick up everything automatically from your credit card details.
Once you get your name changed on your SS card, you can make changes to your name in your respective credit card.
For e.g., if you have bank of america CC, you can go online into your CC account and change your name.

Once you make this change, your credit karma and other private credit score companies will automatically update it with your new name.
Each CC company/bank send update monthly to these private CC scoring companies.

Let me know if you need more information.