"Should this change result in any inconvenience" means "If this change should result in any inconvenience". Here "should" implies that there is not likely to have any inconvenience but just in case , if there actually is some inconvenience, let me know. Similarly,"Had he studied hard, he wouldn't fail the exam" means "If he had studied hard, he wouldn't fail the exam". They are both Inverted sentences.

This is a very typical phrasing in business English. In this example, "should" means "If it happens that..." Other ways of phrasing the sentence are... "If this change results in any inconvenience..." (This is not a good thing to say. It suggests that the inconvenience is very possible.) "In case of this change resulting in any inconvenience..." (Grammatically correct, but it sounds awkward and distant.)

Hi, it means the same as "if" but it's more polite. it's better because "if" is not designed to start a sentence, only a subclause. Consider: "should you wish to take the matter further" means "if you wish". This is very different from the usual meaning of should and is used only in very polite circumstances such as government notices, apologies etc, customer care. Be careful though because it can change your spelling. in your sentence "should this change result..." it becomes "if this change results......" With the s.

this sentence is asking the change of sometihng does or not cause any problems to you. if does, you should tell him or her right now.