You should check phosphate, creatinine (including eGFR) and microalbumin at the very least.
After starting Tenofovir, it would be recommend to check these every 6 months (for those that want to be more safe they might decide to do their first check after 3 months, then keep checking every 6 months thereafter). In the case of a significant worsening of kidney function (this happens to just small number of people taking tenofovir) doctors often recommend tenofovir to be discontinued and replaced with ETV (entecavir).
It would be always nice to have a baseline value of those test results, to compare later values so as to be able to recognise potential changes and then act accordingly.
P.s. On your place I would be paying attention for TAF release (next generation of original Tenofovir which will be coming out soon)...and once it is released in your country look to be switched to it as it is much easier on the kidney and bones in the long run.
At the very minimum, you should always ask for hbvdna(viral load) and ALT (not AST). You should also have a yearly liver function test. After several years, you may also like to ask your doctor to check your kidney function, due to possible side effect from taking Tenofovir.