As Yer_Man says, "name of picture" can mean several things. For instance, the Photos app doesn't care about filenames-- it doesn't even use them, really, but it shows the filename in the Info Window for reference. You can't use Photos to change file names.
Photos uses ITPC, another metadata thing, to record captions, keywords, and titles. The Title (but not the filename, or caption) can be made to show up under pictures in the thumbnail view, and you can sort by title if you want. Doing batch operations with title sequences isn't something Photos does, but there are scripts that do that for you. See this: Thematic Index to Photos for Mac related … - Apple Community --and search for Batch.
There are a number of apps that can change filenames before you add pictures to Photos. An app that many of us use is GraphicConverter ($40) which also makes it easy to add information to Exif metadata and to IPTC metadata. The free ExifTool Reader lets you see the Exif metadata. Be very careful of apps that say they do things like this for pictures within the Photos Library-- they may corrupt the Library.
For batch changing titles within Photos, I use Photos Workbench ($30) which offers all sorts of options for titles. For instance, I include the date at the beginning of titles so that I can sort by title even for pictures whose date isn't really the capture date, and I add sequencing numbers to put them in the order I want.
Let us know if we can help with this....