Here is an expression you can use. It works if your grid is properly ordered, meaning all centroids of one column have the same x coordinate all centroids of one row have the same y coordinate. Note the limitations when using letters instead of numbers: There are only 26 capital letters in the latin alphabet, so your grid should not exceed 26 columns. If you do not want this limitation, take a look at this answer.
with_variable('n_cols',array_distinct(array_agg(x(centroid($geometry)))),
with_variable('n_rows',array_distinct(array_agg(y(centroid($geometry)))),
with_variable('char',array_foreach(generate_series(0,25),char(@element+65)),
@char[array_find(@n_cols,x(centroid($geometry)))]
||
array_find(@n_rows,y(centroid($geometry)))
)))
Result:

How, why and when this works:
This expressions works, if your grid is properly created. Means every centroid of one column has the same x coordinate as every other centroid in this column. Same goes for rows: it works if every centroid has the same y-coordinate as every other centroid of this row.
We are using these coordinates to determine how many columns and how many rows a grid has in total. We need this to properly name rows and columns.
For the naming we just check in at which array position the current centroid coordinate is. For x we are using a letter lookup from A to Z and for y just the number. You could add +1 here if you dont want to start it from 0.
So lets explain the expression:
array_distinct(array_agg(x(centroid($geometry)))) creats an array of all x coordinates of the centroids and keeps only distinct values. The length of the array is the number of colums. The number of rows works the same, just using the y coordinate.
array_foreach(generate_series(0,25),char(@element+65)) creates the letter lookup. char() gets the character from the unicode list, you can lookup here: https://en.wikipedia.org/wiki/List_of_Unicode_characters. A has the value 65. So we start at this position (+65). @element is the current array position of the current centroid coordinate.
PS: I don't know how to explain this better at the moment. If you have a specific question just let me know and I will try to clarify.