How can you search for name in PuTTY? Do you mean by typing the first letter?
In WinSCP, you can do the same. Actually in WinSCP, you can even type multiple leading letters. Or even any part of a hostname (not only leading part).
(look for "incremental search").
I have the exactly site name in Clipboard. Putty hasnt a direct search, but it isnt a problem to insert a site name directly from the Clipboard.
Search site by typing part of its name is good feature. So, insert from Clipboard isnt possible.