Let's say a company have ten branches in different States. Is it require to get multiple regd under GST?

yes...company required to get register in each state from where it is making sales..

I guess, if you have a HO at Mumbai and you invoice all your sales and service from Mumbai, then you do not need to register for other branch offices. Please clarify.

1) YES required to get registration for each branches if all are in different states
2) Without taking new registration you cannot send goods from one branch to another (branch transfer)

if head offfc nd branch offc have different names, then

if head offc nd branch offc had diiferent names then how will ww take new reg .. please help

the gst registration is given on the bases of pan.....if both ho and branch are engaged in similar business and are in same state than single registration will be given....if both ho and branch are in same state but have different type of business than you have option to either take single registration or different registration....if both are in different states than you have no choice but to take sperate registration

and sir how to reg branch under same PAN