How to change the order of photos at Google Photos

Introduction

Photos are sorted in the Photos tab according to "Date taken" (when available).  In albums you can sort by :

There are mainly two reasons to change the order of photos:

 I still use to drag photos in the order I want in Picasa on a computer (having a backup on a computer and at least one more place is a good idea), and rename them in batch with Name-001, Name-002 etc (see further). In Picasa Web Albums we could sort by file name, but Google Photos does not support sorting by file name in an album. That would be a minor change with a big advantage for what they call a minority ("most users don't need this"). 
What remains is:

Measures you can take before uploading

Drag photos in the order you want, and change the filename

Although Google Photos does NOT support sorting by file name, changing the file name as shown below preserves the order when someone downloads the album.  There are many tools to rename multiple photos in batch, but you need to be able to get them first in the order you want, for example by drag & drop.  

You can use for example:

That would be all you need to do, if the Google Photos team did not obstinately refuse to implement sorting by file name.  For mobile phone users, adding a renaming tool (to be used after drag & drop) would make it even better. 

Change date/time (DateTimeOriginal)

To change date/time you can for example use :

Warning:  

Change order after uploading

Go to Google Photos "Albums": https://photos.google.com/albums and open the album you want to organize.

Drag & drop

At the top right, click the 3-dot menu and click "Edit album"
You can drag-and-drop selected pictures to another position.

The changed order is lost after downloading or adding to another album, for example in another Google Photos library.

Click the "Sort Photos" icon (up and down arrows). 

At the top right, click the 3-dot menu and click "Edit album"

You see the options "Oldest first" Newest first" "Recently added (first)". 

When finished, click the check mark ("Done") in the upper left corner. 

Unfortunately, "Sort by filename" is not possible. Please send feedback in Google Photos to ask for that feature.
Third party extension (not tried - at your own risk): see https://github.com/hamada2029/gphotos_sort

Change date/time in Google Photos

Photos in albums can be sorted by date/time. Changing date/time may thus change the order of the photos.
This will also change the order in the Photos tab and other albums where the photo is added. 

This only changes times in the Photos database, not in the EXIF data. Changed dates are lost after downloading, but kept when added to another album or using "Add to library" after sharing.

Warning: there may still be issues when photos in the album have different time zones. The timezone can be adjusted in batch in Google Photos: