workgroup and domain together

When you login as a user to a Domain you must assign this user to a particular workgroup existing on the Domain (or ask your Network admin to do it)

There is a business network (domain name) and a home network (workgroup name). Can we have a domain and workgroup name on this one laptop?

No, its not possible, you have to remove/readd to the domain everytime. See:

http://support.microsoft.com/default.aspx?scid=kb;en-us;228146&Product=ntw40
http://support.microsoft.com/default.aspx?scid=kb;en-us;317049&Product=ntw40

But if you can create a local username on the Laptop to logon to the machine (w/o logging onto the domain) but you will have to browse for the Workgroup.

1st thing
might be possible u need to acces two network on it with domain with different ip and 2nd is workgroup with different ip bind both network ips to you LAN ...

2nd thing
plz see lmhost.sam file and give workgroup computer network name with ip and #net entries to tell this is workgroup computer names etc...