See the below query
insert into Test1.dbo.table_T1(name)
(select name from Test.dbo.table_T1 )
Where Test1 and Test are Two database and both have same table.
I am just fetching data from one table to insert another database table
So format of query is like below
Insert into DatabaseName1.SchemaName.TableName(Column1,Column2)
(Select Column1,Column2 from DatabaseName2.SchemaName.TableName)