MariaDB 10.3

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.

create table t (name varchar(10), description varchar(100));
insert into t values ('b', '"Photo number # - Gallery name"');
insert into t values ('c', '"Photo number # - Gallery name"');
insert into t values ('a', '"Photo number # - Gallery name"');
insert into t values ('x', '"Photo number # - Gallery name"');
update t
join (select 
          name, @num := @num + 1 as num
      from
          t, (select @num := 0) t
      order by
          name) t2
on t2.name = t.name
set description = replace(description, '#', cast(num as varchar(10)));

Rows matched: 4  Changed: 4  Warnings: 0


select * from t order by name;


name
description


a
"Photo number 1 - Gallery name"

b
"Photo number 2 - Gallery name"

c
"Photo number 3 - Gallery name"

x
"Photo number 4 - Gallery name"

name	description
a	"Photo number 1 - Gallery name"
b	"Photo number 2 - Gallery name"
c	"Photo number 3 - Gallery name"
x	"Photo number 4 - Gallery name"