I'm afraid I can't grasp what you're asking. You can not "ignore the file extension". You can turn off the file extension in your operating system, but InDesign only places certain file types. Please give us a better description of what you're trying to do.
The client sent me an Excel table with a few hundred products; a column contains the names of the corresponding photos without the extension (.jpg, .psd, etc.). When I import pictures with Data Merge, InDesign does not recognize pictures in the folder because the photos have not only the name also the extension ... There is a way to tell InDesign to ignore the extension and recognize the file without it? Thanks again
No that I am aware of. ID needs to know the type of the file. Try just dragging one into ID without an extension.
Inspect the files themselves by spot checking several. See what they seem to all be. Or, using an image editor, you may be able to run a batch process that is not image source dependent on the folder and have them output with a common extension. I haven't tried this but it may work. If it does, then amend the spreadsheet to include the extension.