Should contractions be used with first names?
Solution 1:
We do not really have contractions in names. O'Reilly may have its roots in meaning "of the Reilly clan" but Mr. O'Reilly's last name is O'Reilly, not Reilly. Similarly, you should not be shortening people's first names unless you know that's what they want to be called. So if Rebecca introduces herself as Rebecca, you should call her that. If she introduces herself as Becca and doesn't use her fullname, then you may call her that.
Solution 2:
Apostrophes are typically not used in nicknames, because many nicknames do not have an obvious position for the apostrophe. Because many do not, it would be unusual to add it for the ones that make sense, instead of just writing the name as though it's the complete name. Here are some examples of nicknames that wouldn't make sense with an apostrophe:
Rebecca -> Becky
Richard -> Dick
Robert -> Bobby
Katrina -> Kate
It's also the case sometimes that someone's full name is the shortened name. For instance, it's impossible to know if someone that introduces themselves as "Bob" was given a longer name at birth, or if that's the complete name. Best to just use the name as it's introduced to you.