It means that the person is extremely unpopular.
It is a trigger for saying that someone has done a deed which has made him infamous in his circle and where people are angry with the said person.
If you keep hanging out with the local goons then soon your name will be mud too.
The two sisters, Emily and Ruth’s names are mud because of their constant gossiping.
To go to a party with such people and at such an hour can put a young girl’s name in mud.
A child should endeavour to make his parents proud and not put their names in mud.
There is no origin for this idiom
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definition
Common phrase that has a specific meaning.