How to remove the space and dots and convert into lowercase in Pyspark

I have a pyspark dataframe with names like

N. Plainfield
North Plainfield
West Home Land
NEWYORK
newyork
So. Plainfield
S. Plaindield

Some of them contain dots and spaces between initials and some do not. How can they be converted to:

n Plainfield
north plainfield
west homeland
newyork
newyork
so plainfield
s plainfield

(with no dots and spaces between initials and 1 space between initials and name)

I tried using the following but it only replaces dots and doesn't remove spaces between initials:

names_modified = names.withColumn("name_clean", regexp_replace("name", r"\.",""))

After removing the whitespaces and dots is there any way get the distinct values.
like this.

north plainfield
west homeland
newyork
so plainfield