It looks like difficult but from my point of view for this solution, you can use User filter in Data Source or ISMEMBEROF if using Tableau Server.
Please let me explain for this.
1.) Create one column in each data source and put value name of the company like if you have company "Alex" then put "Alex" in all row of new created column and same process with another data source.
2.) Now merge(Union ALL) both data source together and create one table.
3.) now create dashboard and use "User filter" or "Data source Filter" for that column where we have kept name of "company" where you can restrict who can see which data.
I think this can solve your problem.
Please mark helpful if you are able to solve your problem with my solution.
Please let me know if you don't understand my concept. I'll try to explain in different way.
What do you mean by "each data source"
As I mentioned , I only have one data source
and I want to Make Cline based/Company specific dashboards using this data source
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Then Just use ISMEMEBEROF function with "company name" column if working on Tableau server.