As part of my research I have conducted two survey questionnaires where the first one has closed ended questions and the second one has both closed and open ended questions. My doubt was whether to call this a Quantitative or Mixed Methods approach?
You can call it a convergent mixed methods design with survey variant as Cresswell and Plano Clark (2018) noted in the updated typology. However, if the qualitative data is not rich and suitable for rigorous qualitative analysis and you cannot integrate qualitative and quantitative then better label it as a quantitative survey.
I second Ahtisham Younas' remarks. Asking open-ended questions is mixed methods (probably embedded), but in most cases the information will be surface-level and redundant. A major mistake I've seen many times is to just pick out quotes one likes; one must analyze using a qualitative methodology.
I would like to add a little more about my research. The first survey which has closed ended questions is only to check if the participant is eligible and has the knowledge to participate in the second survey which has open ended questions.
In this scenario, in my opinion, a sequential explanatory mixed methods research approach would be best suited.
I had a follow up question to this. If I am using descriptive statistics to analyse quantitative findings and thematic analysis to analyse qualitative findings, then which would be the method for integration?