If you have your databases on different servers you can use two connection strings. But if you have your databases on the same server you can pass database name as a variable to your stored procedure and there you can create a dynamic query. For example:
Create Procedure CompanyDetails
(@companyID int,@databaseName varchar(50))
AS
BEGIN
declare @sql varchar(500)
set @sql = 'select * from ' + '[' + @databaseName +'].dbo.CompanyDetailsTable where companyId = ' + Convert(varchar(10),@companyID)
exec @sql
END