Hi - my name is XXXXX XXXXX X'm a litigation attorney here to assist you.
This is actually a pretty simple legal process. All you need to do is file a petition for name change; inform the court why you want the name change and allege that it is in the child's best interest to have this done.
You will, however, be required to issue process/notice to the father that you're wanting to change the child's last name. If you know where he is, you will have to serve him with a summons to appear. If you don't know where he is, you can publish a summons in the local newspaper to get this done.
Because of the requirement to issue process to the father, I would recommend that you hire an attorney to file this petition on your behalf. However, if you want to try this on your own, there are forms such as the one at the following link: http://www.ilrg.com/forms/namechange-minor/us/mo
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