replacing url shown in browser

Silly question, apologies for my profound ignorance:

Is there a way to get a particular name to show in the
browser address field?

mathopd is responding to http://123.123.123.123 
is there a way for the address field to show
http://big.dog.com

mathopd is responding to http://123.123.123.123/blob
is there a way for the address field to show
http://www.blob.com

Take pity ;-)

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