To open current account of proprietoship concern, nationalised or cooperative bank will open it even if you give an address proof of proprietor and PAN. A proper introduction from a fellow current account holder will also be in order and they may not insist on a registration. You can no doubt make a voluntary registration for VAT or Service Tax but that costs. In VAT you have to make advance payment of VAT and give an NSC as security. In service tax you pay service tax without exemption for services rendered to domestic clients. Normally the ICICI Bank and HDFC Bank ask for VAT or any other registrations in name of proprietorship or a cheque from existing bank account of proprietorship. You open one account in a nationalised bank or cooperative bank and then issue them the cheque from that bank to open the account. I suggest you bank with nationalised bank or cooperative bank having forex first before going to these fancy banks. They will slaughter you with charges down the line.
However, if your turnover exceeds 9 lakhs, registration with Service Tax is compulsory but your service to foreigner is exempt from tax as an export subject to you complying with conditions of bringing remittance to the country etc. Therefore you need the bank account in the name of proprietorship. You cannot register in proprietorship, issue bill in proprietorship and receive payment in individual. Do not get carried away by the fancy banks to have an account in there. Our nationalised banks are far better than them these days. As a suggestion, go the the foreign exchange authorised branch of a smaller nationalised bank. Services are excellent and payments come on time provided your remitter fills the MT 1xx form correctly.
If you have only the foreign income and really are desperate to bank with HDFC or ICICI, then take a voluntary basis registration of service tax. You will have to file returns even if you do not cross the limits.
You could be resident of a state where you are liable to pay professional tax or deduct professional tax on what you pay to employees salary over Rs.3000 per month. You may be liable to deduct TDS on salary over Rs.160,000 per annum paid to anyone in which you can take a TDS registration in your individual name with proprietorship as a branch. You can take enrollment from Proffessional Tax for your business in the name of your proprietorship. You can register under professional tax for deducting from employees. However the enrolment is mandatory if you are doing business or profession, the latter is required only if you qualify. In Incometax you can obtain TAN in name of proprietorship. It is issued to you Individually but your proprietorship name is recorded. I am sure HDFC or ICICI should accept these as proof for proprietorship. Go through these only if you re desperate as you are obliged to file returns if you get these registrations.