how can i search for files and zip them in one zip file

The command you use will run zip on each file separately, try this:

find . -name <name> -print | zip newZipFile.zip -@

The -@ tells zip to read files from the input. From man zip(1),

-@ file lists. If a file list is specified as -@ [Not on MacOS], zip takes the list of input files from standard input instead of from the command line.