"Transactions with the same merchant appear under slightly different names from month to month, meaning that rules do not apply to them (eg my mobile provider appears variously as 3, H3G, 3G...). Is there a way to fix this? "

Glad to see you in the Community forum, @mikemcdonough74.

Creating bank rules in QuickBooks Self-Employed works best when you have the same transactions. However, since this is a read-only app, we are dependent on whatever information that is downloaded from the bank. Thus the reason why rules do not apply to different names, and only to the transactions and categories selected. 

You can always adjust your rules or delete ones you don't need. You may refer to this article for more information: Create rules to speed up reviews in QuickBooks Self-Employed.

Should you have any additional questions or concerns, do let me know. Thanks for reaching out, best wishes.