I have met a couple of shaivites who have vaishnavite names ( ramakrishna, giri, venkatraman) though I have never encountered a vaishnavite family with predominately shaivaite names. Is there any reference in any of our scriptures to this? What is the reason behind this - I.e. Shaivites naming their children after God Vishnu?
One of the names of Vishnu is Shiva as described in this post. Similarly, there is overlapping of many other names too in Shiva Sahasranama and Vishnu Sahasranama. Also, there are many versions of Shiva Sahasranama and Vishnu Sahasranama from various scriptures.
So the vaishnavite names can also be interpreted as Shaivites names or vice versa.
It is safe to say people whom you are referring to are actually Smarthas. Orthodox Shaivaites are rare in modern days. Smarthas on the other hand, are more inclined to follow Smrithi (the Vedas) and accept all forms of god as supreme and equal. Vaishnavism/Vaishnavam/Sri Vaishnavam that Sriman Narayana (Vishnu is his avatar) is the only supreme being (aka Brahman) and other gods are actually Devathas who has Vishnu as their antharyami (paramathma - one who resides inside athmas and is the supreme). So, the answer to your question is that they are Smarthas who are more liberal in naming their children since they worship all gods equally.